Skateboarder on a ramp| Physics

A skateboarder starts up a 1.0-m-high, 30° ramp at a speed of 6.9 m/s. The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air.

A) How far from the end of the ramp does the skateboarder touch down?

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Angular Acceleration| Circular Motion| Physics

Your car tire is rotating at 4.0 rev/s when suddenly you press down hard on the accelerator. After traveling 300 m, the tire’s rotation has increased to 6.5 rev/s . The radius of the tire is 32 cm.

A) What was the tire’s angular acceleration? Give your answer in rad/s²?

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The direction of Velocity at Various Times in Flight for Projectile Motion| University Physics

Alex, a mountaineer, must make it across a wide crevasse. Alex runs horizontally off the edge and successfully makes it to the other side of the crevasse, which is below the point from which he takes off, as shown in the figure.

The figure shows a man running to the right toward a crevasse, which right side is below its left side. The xy-plane is shown. The x-axis is directed to the right, and the y-axis is directed upward.

A) Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the edge of the crevasse.

B) Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he safely lands on the other side of the crevasse.

At the buzzer, a basketball player shoots a desperation shot. The ball goes in!

The figure shows a basketball player holding a ball in front of a basket. The player is to the left of the basket and faces to the right. The ball in his hands is below the basket. The xy-plane is shown. The x-axis is directed to the right and the y-axis is directed upward.

 

C) Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands.

D) Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height.

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Projectile Motion| University Physics

A rock is thrown with a speed of 12.0 m/s and a launch angle of 30.0° (above the horizontal) travels a horizontal distance of d=17.0\:m before hitting the ground. Use the value g=9.800\:m/s^2 for the free-fall acceleration.

A) Which diagram represents an accurate sketch of the rock’s trajectory?

B) Find the height y_i from which the rock was launched.

C) A second rock is thrown straight upward with a speed of 6.000 m/s. If this rock takes 1.636 s to fall to the ground, from what height H was it released?

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Conceptual Problem about Projectile Motion| University Physics

The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0=0\:s corresponds to the moment just after the ball is launched from position x_0=0\:m and y_0=0\:m. Its launch velocity, also called the initial velocity, is \vec{v}.

Two other points along the trajectory are indicated in the figure.

  • One is the moment the ball reaches the peak of its trajectory, at time t_1 with velocity \vec{v}_1. Its position at this moment is denoted by \left(x_1,\:y_1\right) or \left(x_1,\:y_{max}\right) since it is at its maximum height.

  • The other point, at time t_2 with velocity \vec{v}_2, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is \left(x_2,\:y_2\right), also known as \left(x_{max},\:y_2\right) since it is at its maximum horizontal range.

Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which it was launched, as is the case here. Hence y_2=y_0=0\:m.

The parabolic trajectory is shown on the xy plane. The trajectory starts at the origin with coordinates labeled as x 0 and y 0. The initial velocity of the ball is v 0, and it is directed upward and to the right. The initial moment of time is t 0. The object rises to a maximum height y 1 or y max. At this moment of time labeled as t 1, the velocity v 1 is horizontal and directed to the right, and the position of the ball is x 1. Then the ball falls to the ground. It lands at a point that is at distance x 2 or R from the origin. At this moment of time labeled as t 2, the velocity v 2 is directed downward and to the right.

How do the speeds v_0,\:v_1,\:and\:v_2 compare?

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Velocity in a Moving Frame| University Physics

You are attempting to row across a stream in your rowboat. Your paddling speed relative to still water is 3.0 m/s (i.e., if you were to paddle in water without a current, you would move with a speed of 3.0 m/s ). You head off by rowing directly north, across the stream. Assume that the stream flows east at 4.0 m/s, determine how far downstream of your starting point you will finally reach the opposite shore if the stream is 6.0 meters wide.

The figure shows a top view of a rowboat moving in the north direction across a stream. The north direction coincides with the top direction on this figure, and the east direction coincides with the direction to the right on this figure.

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