consider the video you just watched. suppose we replace the original launcher with one that fires the ball…
consider the video you just watched. suppose we replace the original launcher with one that fires the ball upward at twice the speed. we make no other changes. how far behind the cart will the ball land, compared to the distance in the original experiment? view available hint(s) hint 1. determine how long the ball is in the air hint 2. determine the appropriate kinematic expression the same distance four times as far twice as far half as far by a factor not listed above submit previous answers request answer incorrect; try again; 5 attempts remaining the ball will spend more time in the air, which will change how far behind the cart it lands.
Answer
Explanation:
Step1: Analyze vertical - motion time
The time of flight (t) of a vertically - launched object is given by the kinematic equation (v = v_0−gt) for the upward motion. At the maximum height, (v = 0). The time to reach the maximum height (t_{up}=\frac{v_0}{g}), and the total time of flight (T=\frac{2v_0}{g}), where (v_0) is the initial vertical velocity and (g) is the acceleration due to gravity. If the new initial velocity (v_{0_{new}} = 2v_{0_{old}}), the new time of flight (T_{new}=\frac{2v_{0_{new}}}{g}=\frac{2\times(2v_{0_{old}})}{g}=2\times\frac{2v_{0_{old}}}{g}=2T_{old}).
Step2: Analyze horizontal - motion displacement
The horizontal displacement of the ball (x = v_{x}t), where (v_{x}) is the horizontal velocity. The horizontal velocity of the ball and the cart is the same (assuming no air - resistance and the cart moves with a constant horizontal velocity). Let the horizontal velocity of the ball and the cart be (v_x). The displacement of the ball relative to the cart (\Delta x=(v_{x_{cart}} - v_{x_{ball}})t). Since (v_{x_{cart}}=v_{x_{ball}}) in the horizontal direction, and the relative horizontal acceleration is zero. The displacement of the ball relative to the cart depends on the relative horizontal velocity and time. The relative horizontal velocity remains zero throughout the motion. So, the ball will land at the same position relative to the cart.
Answer:
the same distance