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At what angle the projectile must be projected so that time of flight is maximum?


Time of flight =  

For maximum time of flight sin  = 1

So angle of the projectile is 90o
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An object is projected with kinetic energy K at an angle θ. What is the ratio of kinetic energy to the potential energy of the projectile at the highest point?

The ratio of the kinetic energy to the potential energy of projectile at the highest point is cot2θ.
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An object is projected with kinetic energy K at an angle θ. What is the kinetic energy of projectile at the highest point?

Kinetic energy of projectile at the highest point is given by,

K.E = K cos
2θ
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A ball thrown up is caught by the thrower 4 s after start. What is the height to which the ball has risen?

Time of ascent = Time of descent. 

Therefore, 

t1 + t2 = 4

t2 + t2 = 4

This implies, 

t2 = 2 sec

Now, taking vertical downward motion of the ball from the highest point to surface of earth we have, 

u = 0, a = 10 m/s, t = 2 s, s = ? 

Now, using the formula,

                      s = ut + 1/2 at2

                         =  
                         = 20 m

This is the height to which the ball has risen. 

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What is the angle between instantaneous velocity and acceleration at the highest point of trajectory?

At the highest point of trajectory, velocity becomes zero. 

So, the angle between instantaneous velocity and acceleration at the highest point of trajectory is 90°.
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