A ball is fired from the y = 0 level and the motion continues until the ball ret

Question

A ball is fired from the y = 0 level and the motion continues until the ball returns to y = 0. The range is the maximum horizontal distance traveled, and the time-of-flight is the time the ball is in motion. With no air resistance, how does doubling the initial velocity of the projectile affect its range, time-of-flight, and the maximum height reached. Doubling the velocity ________________________ (what happens to range, TOF, and max height?).

Start with air resistance turned off. Confirm that the time the projectile takes to reach its maximum height is the same as the time it takes to fall from the maximum height position back down to ground level. Which of the following statements correctly compares these times when air resistance is turned on?
a. the time to reach max height is smaller than the time to fall to ground level from the max height point b/c the avg vertical speed of the projectile on the way up is larger than its avg vertical speed on the way down
b. the time to reach max height is still the same as the time to fall from the max height position back down to ground level b/c the net force has been increased by the same amount going up as it has going down
c. the time to reach max height is longer than the time to fall to ground level from the max height position b/c the avg vertical speed of the projectile on the way up is larger than its avg vertical speed on the way down

Explanation / Answer

x distance=Vo²/g*sin(2*)==>max ht=voy²/(2*g)==>max ht t=voy/g

doubling the Vo will more than double the range, and max ht

will double TOF

With air resistance, the max ht is less, the max ht t is less, the range is less,

free fall from a cliff is longer, horizontal shot from a cliff has a shorter range,

longer TOF, etc.

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