Question

If a body is projected horizontally from a height of 50 m with a speed of 20 m/s, then its speed after a time of 1.5 s is
(Acceleration due to gravity \( g = 10\ \text{m/s}^2 \))

• A. 25 m/s
• B. 28 m/s
• C. 15 m/s
• D. 30 m/s

Hint:

In horizontal projectile motion, horizontal velocity remains constant, and vertical velocity increases linearly with time due to gravity. Use \( v = \sqrt{v_x^2 + v_y^2} \) to get resultant speed.

Answer 1

The Correct Option is A

Step 1: Analyze motion components.
The body moves horizontally with constant speed (20 m/s) and vertically under gravity (initial vertical velocity = 0). Step 2: Calculate vertical velocity after 1.5 s.
\[ v_y = g t = 10 \times 1.5 = 15\ \text{m/s} \] Step 3: Calculate resultant speed using Pythagoras theorem.
\[ v = \sqrt{v_x^2 + v_y^2} = \sqrt{20^2 + 15^2} = \sqrt{400 + 225} = \sqrt{625} = 25\ \text{m/s} \]