Two balls are kicked upward at different angles. Ball A travels a greater horizo
ID: 1424504 • Letter: T
Question
Two balls are kicked upward at different angles. Ball A travels a greater horizontal distance than ball B. Both reach the same maximum height. Which of the following statements about the balls are true? Select all that apply.
Question 2 options:
The horizontal (x) component of their velocities are the same.
The vertical (y) component of their velocities are the same.
Ball A has a larger initial velocity than ball B.
Both balls are in the air for the same amount of time.
Ball B has a larger velocity at its maximum height than ball A has at its maximum height.
The horizontal (x) component of their velocities are the same.
The vertical (y) component of their velocities are the same.
Ball A has a larger initial velocity than ball B.
Both balls are in the air for the same amount of time.
Ball B has a larger velocity at its maximum height than ball A has at its maximum height.
Explanation / Answer
if initial velocity is v and launch angle is theta,
then maximum height is given by v^2*sin^2(theta)/(2*g)
as both of the balls have same maximum height, for both the balls v*sin(theta) is same
hence their vertical component of velocities are same.
hence option 2 is correct.
time taken for the whole trip =2*v*sin(theta)/g
as for both the balls, v*sin(theta) are same, both the balls are in air for same time periof
hence option 4 is correct.
horizontal range=v*cos(theta)*time taken
as time taken is same for both the balls, and horizontal distance for A is greater than horizontal distance for B,
v*cos(theta) for A is greater than v*cos(theta) for B
i.e. horizontal component of velocity of A is greater than horizontal component of velocity of B
hence total velocity of A is greater than total velocity of B
(as total velocity=sqrt(horizontal velocity^2+vertical velocity^2))
hence third option is correct
so otpino 2,3 and 4 are correct.