Question

A stone is projected in air. Its time of flight is 3 s and
range is 150 m. Maximum height reached by the stone is
(g = 10 ms?)
(a) 37.5 m
(b) 22.5 m
(c)90 m
(d) 11.25 m​

Answer 1

Answer:-

Given:-

Time of flight 'T' = 3 seconds.

and, range 'R' = 150m.

Case-1

Time of flight.

$t = \frac{2u \sin( \alpha ) }{g}$

substitute the values.

$3 = \frac{2u \sin( \alpha ) }{10}$

$u \sin( \alpha ) = 15 \: \frac{m}{s} \: \: \: \: \: \: \: - - - (1)$

Case-2

Range

$r = 2 {u}^{2} \sin( \alpha ) \cos( \alpha ) \div g$

substituting the values.

as u sin alpha is 15m/s.

$150 = 15 \times 2u \cos( \alpha ) \div 10$

$\frac{100}{2} = u \cos( \alpha ) = 50$

But we need only u sin (alpha) as it is involved in height of the projectile.

Now,Height

$h = \frac{ {u }^{2} { \sin( \alpha ) }^{2} }{2g}$

$h = {15}^{2} \div 20$

$h = \frac{225}{20}$

$h = 11.25 \: metres$

so, 4th option is correct as the height of the projectile is 11.25 meters.