3-8 CHAPTBR 3 Vectors and Motion in Two Dimensions 3.7 Projectile Motion: Solvin

Question

3-8 CHAPTBR 3 Vectors and Motion in Two Dimensions 3.7 Projectile Motion: Solving Problems 38. a. A cart rolling at constant velocity fires a ball straight up. When the ball comes down, wil it land in front of the launching tube, behind the launching tube, or directly in it? Explain. b. Will your answer change if the cart is accelerating in the forward direction? If so, how? 39. Four balls are simultaneously launched with the same speed from the same height h above the ground. At the same instant, ball 5 is released from rest at the same height. Rank in order, from shortest to longest, the amount of time it takes each of these balls to hit the ground. (Some may be simultaneous.) 5 Order: Explanation 40. Rank in order, from shortest to longest, the amount of time it takes each of these projectiles to hit the ground. (Some may be simultaneous.) 100 g 100 g 100 g 200 g 100 g 0 m/s 20 m/s 10 m/s 10 m/s 10 m 10 m 10 m 10 m Order: Explanation

Explanation / Answer

38 a) The ball will land directly on top of the launching tube.

Explanation: Both the cart and ball are moving at the same horizontal speed. After the ball is launched, gravity only changes the vertical velocity of the ball. The horizontal speed of the ball remains the same. So, the cart will cover the same distance horizontally as the ball has covered during its flight in air. Hence the ball will land directly on top of the launching tube.

b) If the cart is accelerating in the forward direction, then the ball will land behind the launching tube.

Explanation: In this case, the horizontal speed of the cart increases after the ball in launched since the cart is accelerating. So by the time the ball comes down, the cart covers more distance than the ball and the ball lands behind the cart.

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39) The time each ball takes to hit the ground only depends on the initial vertical speed of the balls. The more downward vertical speed the ball has, the shorter it will take to hit the ground.

Ball 4 has highest initial downward vertical speed. Followed by ball 3. Followed by ball 2 and 5 which have zero vertical speed intitally. Followed by ball 1 has upward vertical speed.

So the ranking from shortest to longest time taken to hit the ground is

Ball 4(shortest time taken).

Ball 3

Ball 2 and Ball 5( They take the same time to hit the ground)

Ball 1 (Longest time taken)

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40) Balls 1 to 4 have the same initial vertical speed(which is zero). Ball 5 has to cover more distance. Hence the ranking from shortest to longest time taken to hit the ground is

Ball 1 = Ball 2 = Ball 3 = Ball 4(They take the same time)

Ball 5 (Takes longer time since it has to cover more distance)

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