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If T is the total time of flight, h is t...

If T is the total time of flight, h is the maximum height and R is the range for horizontal motion, the x and y coordinates of projectile motion and time t are related as

A

`y = 4h((t)/(T))(1-(t)/(T))`

B

`y = 4h ((X)/(R )) (1-(X)/(R ))`

C

`y = 4h ((T)/(t) (1-(T)/(t))`

D

`y = 4h ((R )/(X)) (1-(R )/(X))`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`T = (2u_(y))/(g) rArr x = u_(x)t R = (2u_(x)u_(y))/(g)`
(A) `y = u_(y)t - (1)/(2)g t^(2) rArr y = u_(y)t (1-(g t)/(2u_(y)))`
`y = u_(y)t (1-(t)/(2u_(y)//g)) rArr y = (u_(y)t)/(T) xx (2u_(y))/(g) (1-(t)/(T))`
`y = (2u_(y)^(2))/(g) xx (t)/(T) (1-(t)/(T)) rArr y = 4 ((u_(y)^(2))/(2g)) xx (t)/(T) (1-(t)/(T))`
`rArr y = 4h ((t)/(T)) (1-t//tau)`
(B) `y = 4h ((t)/(T)) (1-(t)/(T))`
`y = 4h ((x)/(u_(x)xx(2u_(y))/(g))) (1-(x)/(u_(x)xx(2u_(y)//g)))`
`rArr y = 4h ((x)/(R )) (1-(x)/(R ))`
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