A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the projectile is ____ m/s.

Solution

Physics sir · 4 steps

Gravity only pulls down, so the horizontal velocity stays the same all the way through the flight.

1. What stays constant. In flight, the only force is gravity, and it acts vertically. So the horizontal component of velocity never changes from launch to landing.
2. Two moments, one component. At launch the horizontal component is u cos 60°. At the 45° moment it is 20 cos 45°. These two must be equal.

   u cos 60° = 20 cos 45°

3. Put in numbers. u × 1/2 = 20 × 1/√2 = 10√2, so u = 20√2 m s⁻¹.
4. So. The initial speed is 20√2 m s⁻¹, which is option (b).

The idea to keep. When a projectile question gives the speed at some angle mid-flight, match the horizontal components. That is the one quantity that never changes.

Answer from the NTA final answer key. Solution by PrepWiser.