To determine how high the body will go and when it will return to the point of projection, we can use the equations of motion.
Let's denote: Initial velocity (u) = 21 m/s (positive because it's thrown upwards) Final velocity (v) = 0 m/s (at the highest point and when it returns to the point of projection) Acceleration (a) = -10 m/s² (negative because it acts in the opposite direction of motion due to gravity) Displacement (s) = ?
We can use the equation:
v² = u² + 2as
Substituting the values:
0² = (21 m/s)² + 2(-10 m/s²)s
0 = 441 m²/s² - 20s
20s = 441 m²/s²
s = 441 m²/s² / 20
s ≈ 22.05 m
Therefore, the body will reach a maximum height of approximately 22.05 meters.
To find the time it takes to reach the maximum height and return to the point of projection, we can use the equation:
v = u + at
Substituting the values for the upward motion:
0 = 21 m/s - 10 m/s² t₁
10 m/s² t₁ = 21 m/s
t₁ = 21 m/s / 10 m/s²
t₁ = 2.1 s
Since the upward journey takes 2.1 seconds, the total time for the body to return to the point of projection will be twice that, as the upward and downward journeys take equal time:
Total time = 2 * t₁ = 2 * 2.1 s = 4.2 s
Therefore, it will take approximately 4.2 seconds for the body to return to the point of projection.