A particle is projected from the surface of earth with an initial speed of 4.0km/s. Find the maximum height (inkms) attained by the particle.Correct answer is '935'. Can you explain this answer?

Question

Answer

Given:
Initial speed of the particle, u = 4.0 km/s
Acceleration due to gravity, g = 9.8 m/s^2 (approximate value)

To Find:
Maximum height attained by the particle

Assumptions and Approach:
1. We assume that there is no air resistance acting on the particle.
2. We can use the equations of motion to solve this problem.
3. The particle is projected vertically upwards, so the vertical motion is only affected by gravity.

Solution:
1. Convert the initial speed into SI units.
Initial speed, u = 4.0 km/s = 4000 m/s

2. Use the equation of motion to find the time taken to reach the maximum height.
Final velocity, v = 0 m/s (at the maximum height)
Acceleration, a = -g (opposite to the direction of motion)
Using the equation v = u + at, we can write:
0 = 4000 - 9.8t
Solving for t, we get:
t = 4000/9.8 = 408.16 s (approximate value)

3. Use the equation of motion to find the maximum height.
Using the equation s = ut + (1/2)at^2, we can write:
s = 4000 * 408.16 + (1/2) * (-9.8) * (408.16)^2
Simplifying the equation, we get:
s = 1632640 + (-798145.9)
s = 834494 m

4. Convert the maximum height into kilometers.
Maximum height = 834494 m = 834.494 km

Answer:
The maximum height attained by the particle is 834.494 km (approximately 835 km).

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