AP Physics 1 : AP Physics 1

Study concepts, example questions & explanations for AP Physics 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #341 : Newtonian Mechanics

A cannon ball is fired at an angle of 45 degrees from the horizontal. Which of the following describes the kind of motion experienced by the cannon ball in the y-axis and the x-axis respectively?

Possible Answers:

y-axis: motion with constant acceleration and x-axis: motion with constant velocity

Y-axis: motion with constant velocity and x-axis: motion with constant acceleration

Y-axis: motion with constant velocity and x-axis: motion with constant velocity

Y-axis: motion in free fall and x-axis: motion with constant acceleration

Y-axis: motion with constant acceleration and x-axis: motion in free fall

Correct answer:

y-axis: motion with constant acceleration and x-axis: motion with constant velocity

Explanation:

The cannon ball has a two-dimensional motion, specifically projectile motion. Any two-dimensional motion consists of two one-dimensional motions happening at the same time. This is why we break vectors into components, so we can analyze each one-dimensional motion separately. The motion in the y-axis and the x-axis are connected by the time variable, since they happen at the same time. For projectile motion, we have that on the y-axis (the vertical axis) a constant acceleration (gravity) is acting on the cannon ball. For the y-axis motion with constant acceleration or free fall (which is motion with constant acceleration where the acceleration is gravity) are correct choices. On the x-axis (the horizontal axis), there is no acceleration acting on the cannon ball horizontally. Therefore, on the x-axis the cannon ball experiences motion with constant velocity. Then the only answer choice that describes the motion of the cannon ball in each axis correctly is: y-axis: motion with constant acceleration and x-axis: motion with constant velocity.

 

Example Question #101 : Linear Motion And Momentum

An object weighing 15kg is fired from 30m above the ground at an angle of  to the horizontal with an initial velocity of . Determine how long it takes the object to reach its maximum height. Ignore friction.

Possible Answers:

Correct answer:

Explanation:

At the projectile's maximum height, we know that it's vertical velocity will be  Since the only type of acceleration the object faces is the acceleration due to gravity, we can model its velocity using only two terms: it's initial velocity and acceleration due to gravity.  Recall that the formula for velocity with constant acceleration is given as:

Here,  is the object's constant acceleration,  is the initial velocity, and  is time. 

The only acceleration is acceleration due to gravity, which is:

  

To determine initial velocity , we have to determine a few other things. The object is being launched at a speed of  at an angle of . Therefore, the vertical component (the vertical velocity of this object) is going to be 

Therefore, we can model the velocity of this object as:

The signs of the two terms must be opposite because they are going in different directions. Negative velocities in this model mean the object is moving towards the center of the earth. 

Since the object reaches its maximum point when  we must solve the following equation for 

Example Question #11 : Motion In Two Dimensions

A 2 kg cat is stuck in a 10 meter high tree. Just as a fire fighter atttempts to save the cat, the cat slips and falls out of the tree. Luckily, Superman is standing only 3 kilometers away and sees the cat fall. Assuming Super man has instananeous reactions and begins running towards the cat just as it falls, how fast does Superman have to run in order to catch the cat before it hits the ground?

Possible Answers:

Correct answer:

Explanation:

Superman needs to cover 3,000 meters. But the question is how much time does he have to cover those 3,000 meters? If you know the time, you can just divide 3,000 meters by the time he is traveling and you have his speed! But how do we know how quickly he needs to cover the 3,000 meters? The falling cat tells us! The acceleration due to gravity is a constant on the surface of Earth and it will dictate how quickly something hits the ground once dropped. Considering we ignore air resistance in physics 1, we don't care about the object's size or mass. So all we need to do is find the appropriate kinematic equation(these equations relate displacement, velocity, acceleration and time) and solve for time. The way I chose a kinematic equation is I organize variables into things we are told in the problem and things we are not told in the problem. In this case, we are given information about the height of the cat, it's mass and that it slipped (velocity in both x and y directions is zero). Not much to go off of but it is all we need! We are solving for time and we have information about initial velocity and displacement.

The equation: 

We can see with this equation that under the assumption that the initial velocity is zero, it simplifies to a relationship between x and t (acceleration is g and is a constant). Rearranging for t gives: 

Plugging in the appropriate numbers, the time that it take for the cat to hit the ground will be 1.43 seconds. Now we know Superman must cover the 3,000 in 1.43 seconds.

Dividing 3,000 by 1.43 yelids a velocity of  

Example Question #14 : Motion In Two Dimensions

A cannon is fired from the top of a  cliff as shown in the figure below. If the cannonball travels a horizontal distance  of  in , at what angle was the cannon fired? (Hint: Find an expression for . You do not need the initial velocity to solve this.)

Projectile1

Possible Answers:

Correct answer:

Explanation:

At first this problem could seem challenging, but in fact, it is straight-forward if you can remove the initial velocity from the equations.  We begin by writing the equations of motion for the x and y directions.

We then devide the two equations to get an expression for the tangent of the angle, as well ass remove the initial velocity from the problem.  This enables us to use the information given to calculate the angle the projectile was fired.

Example Question #12 : Motion In Two Dimensions

Determine how long it takes a car to move up a  incline, with its top at  above the ground if its speed is constant at 

Possible Answers:

Correct answer:

Explanation:

The top of the hill is  above the ground. However, that isn't the distance from the bottom of the hill to the top, since the car is going up an incline of

The length of the incline can be given as: 

, where  is the length of the incline. 

Solving for 

The incline is  in length. 

At a speed of 

Example Question #15 : Motion In Two Dimensions

A projectile is shot at  above the horizontal at a velocity of . How high does the projectile travel at its peak?

Possible Answers:

Correct answer:

Explanation:

First we need to find the vertical velocity component (y-component). We know our velocity is  at an angle of . We need to use the sine function to determine the y-component:

Now we use the kinematic equation to determine the height reached:

We solve for  which is our height and substitute our known values.

Our initial vertical velocity is  and final vertical velocity is  at the peak.

Example Question #111 : Linear Motion And Momentum

A projectile from a hand gun is fired at  above the horizontal at a speed of . How many seconds is the projectile airborne? Assume  and that the hand gun was fired a negligible distance from the ground.

Possible Answers:

None of these

Correct answer:

Explanation:

Since the question is asking how long the projectile was airborne, we are dealing with motion in y-direction only. Find initial velocity in the y-direction and substitute into the kinematic equation:

Example Question #12 : Motion In Two Dimensions

A medieval cannon fires its projectile horizontally from a castle wall 70 meters high at a speed of . How long will the cannonball be airborne?

Possible Answers:

Correct answer:

Explanation:

Narrow the choices of kinematic equations by including only ones with distance in their formulas. Of those two, we want the one that includes time:

 

The red term becomes zero because our projectile is not moving at first. Plug in known values and solve.

Example Question #21 : Motion In Two Dimensions

An archer fires an arrow horizontally off a 60 meter high castle wall at a speed of . What is the closest you could stand to the castle wall without fear of being hit?

Possible Answers:

Correct answer:

Explanation:

Find the time the object is airborne by solving for t in the equation:

Then, multiply the time in the air by the initial velocity to get the range of the projectile. Note that the initial velocity is zero in the y-direction.

Example Question #21 : Motion In Two Dimensions

 force pushes a  block, from rest,  across a frictionless table that is  above the floor. If the force stops acting on the block when it leaves the table, calculate how far  the block lands from the table.

Possible Answers:

Correct answer:

Explanation:

This is a two-part problem. First, we need to know how fast the block is moving in the horizontal direction when it leaves the table. This can be calculated by using a kinematic equation, combined with Newton's second law.

Now that we know how fast the block is moving horizontally, we need to know how long the block will be in air before hitting the ground. This is found by considering the equations of motion for an object falling from rest:

Lastly, we find the horizontal distance by:

Learning Tools by Varsity Tutors