If a projectile is thrown obliquely both at earth and moon and the angle of projection with the horizontal and the initial speed of throw is same in both earth and moon then which projectile will cover the maximum height?

1 Answer
Aug 11, 2017

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Maximum height is reached when sin thetasinθ component of the velocity of projectile becomes 0 (zero)
Use the kinematic formula

v^2-u^2=2ghv2u2=2gh

Since force of gravity is acting against the direction of vertical component of initial velocity so it is deceleration.
Substituting various values

0^2-(usintheta)^2=2(-g)h02(usinθ)2=2(g)h
=>h=(u^2sin^2theta)/(2g)h=u2sin2θ2g

Acceleration due to gravity on the Earth is =9.81ms^-2=9.81ms2 and acceleration due to gravity on the surface of the Moon is =1.625 ms^-2=1.625ms2

From the derived expression for maximum height we see that for same initial velocity and same angle of projection

hprop1/gh1g

=> Maximum Height attained on moon will be greater.