A body is projected vertically upwards from the ground such that its speed at half the maximum height is 20m/s. Find the maximum height attained by it.
To find the maximum height attained by the body, we can use the concept of projectile motion.
Let's break down the problem step by step:
Step 1: Identify the given information:
- Initial velocity (u) = ?
- Final velocity (v) = 0 m/s (at the maximum height, the body momentarily comes to rest)
- Acceleration (a) = -9.8 m/s² (assuming gravity acts downward and is uniform near the Earth's surface)
- Speed at half the maximum height = 20 m/s
Step 2: Find the initial velocity:
To do this, we can use the equation of motion:
v² = u² + 2as
Since the final velocity is 0 m/s at maximum height, the equation becomes:
0 = u² + 2as
Substituting the known values, we get:
0 = u² + 2(-9.8)(h/2)
0 = u² - 9.8h
Simplifying the equation, we find:
u² = 9.8h
Step 3: Substitute the given information into the equation:
From the problem, we know that the speed at half the maximum height is 20 m/s. Let's substitute this value into the equation:
20² = 9.8h
Simplifying, we have:
400 = 9.8h
Step 4: Solve for the maximum height:
To find h, divide both sides of the equation by 9.8:
h = 400 / 9.8
h ≈ 40.82 meters (rounded to two decimal places)
Therefore, the maximum height attained by the body is approximately 40.82 meters.