Question

If a pebble is thrown vertically upwards from the top of a tower with velocity 5 m/s. It strikes the ground after 3 seconds. With what velocity the pebble strikes the ground? (take g = 10 ms\(^{-2}\))

• A. 10 m/s
• B. 20 m/s
• C. 25 m/s
• D. 30 m/s

Hint:

For projectile motion problems, consistently applying a sign convention is crucial. Choosing 'up' as positive and 'down' as negative is a standard convention that helps avoid confusion with the signs of velocity and acceleration.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the initial upward velocity of a pebble thrown from a tower, the total time of flight, and the acceleration due to gravity. We need to find the final velocity just before it hits the ground.

Step 2: Key Formula or Approach:
We can use the first equation of motion for an object under constant acceleration:
\[ v = u + at \]
where \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time.

Step 3: Detailed Explanation:
Let's establish a sign convention. We will consider the upward direction as positive and the downward direction as negative.
- Initial velocity, \(u = +5\) m/s (since it's thrown upwards).
- Acceleration, \(a = -g = -10\) m/s\(^2\) (gravity acts downwards).
- Time of flight, \(t = 3\) s.
Now, substitute these values into the equation of motion:
\[ v = 5 + (-10)(3) \]
\[ v = 5 - 30 \]
\[ v = -25 \text{ m/s} \]
The negative sign indicates that the final velocity is in the downward direction. The question asks for the velocity with which it strikes, and the options are all positive, implying we need to find the speed.
The speed of striking the ground is \(|v| = 25\) m/s.

Step 4: Final Answer:
The pebble strikes the ground with a velocity of 25 m/s.