Question

Ron hits a tennis ball straight upwards with an initial speed that is double the initial speed of a ball hit by Luis. A 3rd student thinks Ron's projectile will go twice as high because the initial speed was double. Why is the 3rd student wrong? .

Answer 1

Answer:

height is 4 times

Explanation:

speed of ball hit by Luis is u

speed of ball hit by Ron is 2u

Let the maximum height traveled by the ball hit by Luis is h and by the ball hit by Ron is h'

At maximum height, the final velocity of ball is zero in both the cases.

Use third equation of motion, we get

For Luis :

$v^{2}=u^{2}-2gh$

$0^{2}=u^{2}-2gh$

$h=\frac{u^{2}}{2g}$    .... (1)

For Ron :

$v^{2}=u^{2}-2gh$

$0^{2}=4u^{2}-2gh'$

$h'=\frac{4u^{2}}{2g}$    .... (2)

Divide equation (2) by equation (1), we get

$\frac{h'}{h}=4$

h' = 4 h

Thus, the statement of third student is wrong.