To solve this problem, we can use the equations of motion for vertical motion under constant acceleration.
Let's consider the following variables:
- u = initial velocity = 80 m/s (upward)
- v = final velocity = ? (downward)
- s = displacement = -100 m (negative because the object is moving downward)
- a = acceleration = -9.8 m/s² (acceleration due to gravity, downward)
- t = time taken to reach the ground = ?
We can use the equation of motion:
v^2 = u^2 + 2as
Substituting the known values:
v^2 = 80^2 + 2(-9.8)(-100) v^2 = 6400 + 1960 v^2 = 8360 v ≈ 91.42 m/s
The final velocity of the object when it strikes the ground is approximately 91.42 m/s (downward).
To find the time taken to reach the ground, we can use the equation:
v = u + at
Substituting the known values:
91.42 = 80 - 9.8t 9.8t = 80 - 91.42 9.8t ≈ -11.42 t ≈ -11.42 / 9.8 t ≈ -1.166
Since time cannot be negative in this context, we discard the negative value. Therefore, the time taken for the object to reach the ground is approximately 1.166 seconds.