Question

A body is thrown vertically upwards with a velocity of 35 ms−1 from the ground.The ratio of the speeds of the body at times 3 s and 4 s of its motion is:

• A. \( 3:4 \)
• B. \( 1:1 \)
• C. \( 2:1 \)
• D. \( 3:2 \)

Hint:

For a projectile thrown vertically, the speed at a given time \( t \) during ascent is equal to its speed at \( t \) during descent at the same height.

Answer 1

The Correct Option is B

Step 1: Using the Velocity Equation 
The velocity at any time \( t \) for a body thrown vertically upwards is given by: \[ v = u - g t. \] Given: \[ u = 35 \ ms^{-1}, \quad g = 10 \ ms^{-2}. \] Step 2: Calculating Velocities at \( t = 3s \) and \( t = 4s \) 
At \( t = 3s \): \[ v_3 = 35 - (10 \times 3) = 35 - 30 = 5 \ ms^{-1}. \] At \( t = 4s \): \[ v_4 = 35 - (10 \times 4) = 35 - 40 = -5 \ ms^{-1}. \] Since speed is the magnitude of velocity: \[ |v_3| = 5 \ ms^{-1}, \quad |v_4| = 5 \ ms^{-1}. \] Step 3: Finding the Ratio 
\[ \frac{|v_3|}{|v_4|} = \frac{5}{5} = 1:1. \] Step 4: Conclusion 
Thus, the ratio of the speeds is: \[ \mathbf{1:1}. \]