Chapter 4: Two-Dimensional Kinematics Selected Solutions

Selected Solutions

3. (a) If we take the car's horizontal motion to be the positive x-direction, the x component of its acceleration is

Since it starts from rest, v₀ = 0, the equation for the horizontal distance traveled is

(b) The car's vertical acceleration is

The expression for the vertical distance traveled is

11. (a) Since there is no horizontal acceleration, the time it takes the ball to reach the catcher is

The ball is thrown horizontally, so v_0y = 0. The expression for the distance fallen is, therefore

so it falls a distance of 1.6 m before reaching the catcher.

(b) If v_x increases then t will decrease since . If the time the ball travels is less, the drop distance decreases since .

(c) The moon's gravity is less, therefore the drop distance decreases.

25. Since we know the horizontal distance that it travels and the time, we can determine its horizontal speed

.

This x-component of the intial velocity, together with its direction, can be used to find the initial speed

.

37. If we take her initial vertical position to be y₀ = 0, and note that v_oy = v₀ sinq, her final position is given by

Therefore, the girl was 10.5 m above the water when she let go.

47. (a) At the lava's maximum height, v_y = 0. We can use the equations of accelerated motion assume that the lava is ejected vertically,

(b) Since we know that , the maximum height reached by the lava would be less on Earth due to Earth's greater gravity.

Selected Solutions by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.

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