Question

A body is projected at angle 30° to horizontal on a planet with a velocity of 80 ms-' its time of fligh
is 4 seconds then acceleration due to gravity on that planet is
1) 2ms-2
2) 5 ms-2
3) 10 ms-2
4) 20 ms-2​

Answer 1

Given : T(time of flight) = 4 sec. , u = 80m/s and θ = 30°.

⇒ Time of flight ⇒ T = 2u (sinθ) / g

⇒ g = 2u (sinθ) / T

On putting the values we get,

⇒ g = 2 × 80 × (sin30°) / 4

⇒ g = 40 × 1 / 2 = 20.  [sin 30° = 1/2]

⇒ g = 20 m/s²

Therefore answer will be (4) 20 m/s².

Answer 2

Given : T(time of flight) = 4 sec.

            u = 80m/s

            and θ = 30°.

To Find : Acceleration due to gravity on that planet.

Explanation:

T(time of flight) = 4 sec. , u = 80m/s and θ = 30°.

Time of flight

$\[T{\text{ }} = {\text{ }}\frac{{2u{\text{ }}\left( {sin\theta } \right)}}{g}\]$

$\[g{\text{ }} = {\text{ }}\frac{{2u{\text{ }}\left( {sin\theta } \right)}}{T}\]$

On putting the values we get,

$\[g{\text{ }} = {\text{ }}\frac{{2{\text{ }} \times {\text{ }}80{\text{ }} \times {\text{ }}\left( {sin30^\circ } \right)}}{4}\]$

$\[g{\text{ }} = {\text{ }}\frac{{40{\text{ }} \times {\text{ }}1}}{2}{\text{ }} = {\text{ }}20.\]$                                                  

 g = $\[{\text{20 m/}}{{\text{s}}^2}.\]$

Hence, Acceleration due to Gravity on that planet is $\[{\text{20 m/}}{{\text{s}}^2}.\]$