Question

The time of flight of a vertically projected stone is 8 s. The position of the stone after 6 s from the ground is

• A. \( 20 \, \text{m} \)
• B. \( 60 \, \text{m} \)
• C. \( 75 \, \text{m} \)
• D. \( 40 \, \text{m} \)

Hint:

For projectile motion, use kinematic equations to find the position at any given time.

Answer 1

The Correct Option is B

We are given the time of flight is 8 s, and the acceleration due to gravity is \( 10 \, \text{m/s}^2 \). The time taken to reach the ground is given by: \[ T = 8 \, \text{s} \] The time taken to reach the point after 6 seconds is the remaining time for the upward motion, so: \[ t = 6 \, \text{s} \] For vertical motion under gravity, we can use the following kinematic equation: \[ h = ut + \frac{1}{2} g t^2 \] where \( h \) is the height, \( u \) is the initial velocity, \( g \) is the acceleration due to gravity, and \( t \) is the time. We can calculate the position of the stone after 6 seconds. Using the equation of motion, the position after 6 seconds is: \[ h = 60 \, \text{m} \]

Answer 2

Given:
Time of flight = 8 s (which implies total time to go up and come down)
Time after projection = 6 s
Use \( g = 10 \, \text{ms}^{-2} \)

Step 1: Determine time to reach the highest point
\[ \text{Time to top} = \frac{8}{2} = 4 \, \text{s} \]

Step 2: Analyze motion after 4 s (falling down)
After 4 seconds, the stone is at the highest point, and then it starts falling.
Time of fall = \( 6 - 4 = 2 \, \text{s} \)

Step 3: Use equation of motion to find height from top
\[ s = \frac{1}{2} g t^2 = \frac{1}{2} \times 10 \times (2)^2 = 5 \times 4 = 20 \, \text{m} \]

Step 4: Find total height of the projectile
\[ H = \frac{1}{2} g t^2 = \frac{1}{2} \times 10 \times (4)^2 = 5 \times 16 = 80 \, \text{m} \]

Step 5: Position from ground after 6 seconds
\[ \text{Height from ground} = 80 - 20 = 60 \, \text{m} \]

Final Answer:
\[ \boxed{60 \, \text{m}} \]