Question

What should be the angle of projection from horizontal, so that a
body may cover (1) Maximum vertical distance and (2) Maximum
horizontal distance.​

Answer 1

for maximum vertical distance angle of projection should be 90° from group

for maximum horizontal distance angle of projection should be 45 from the group

Answer 2

Answer:

At an angle=90°, sin ratio has maximum value. So vertical height of projectile is max for 90°.

And about the shortest time, the acceleration due to gravity is same for all objects, so the time of flight for a given angle and intial velocity is always same.

However, considering air resistance, acceleration would be affected by the surface area. So a streamlined body returns faster than any object with large cross section.

As T=(2×u×sin(theta))/g

The minimum value of sin ratio is zero, so minm time of flight is zero at 0°.

So that leads to the conclusion of max vertical height at 90°, minium time at 0°. You can look at either of the variables separately. But, I don't seem to have a perfect answer to combine both at the time.