Explanation:
For projectile motion, use constant acceleration equation:
Δx = v₀ t + ½ at²
where Δx is the displacement,
v₀ is the initial velocity,
a is the acceleration,
and t is time.
For the first object:
Δx = 60 t + ½ (-10) t²
Δx = 60 t − 5 t²
For the second object:
Δx = 0 (t−10) + ½ (-10) (t−10)²
Δx = -5 (t−10)²
When they meet, they have the same displacement, so:
60 t − 5 t² = -5 (t−10)²
60 t − 5 t² = -5 (t² − 20t + 100)
60 t − 5 t² = -5 t² + 100 t − 500
60 t = 100 t − 500
40 t = 500
t = 12.5
Plug into either of the original equations to find the displacement.
Δx = -5 (t−10)²
Δx = -5 (12.5−10)²
Δx = -31.25
The distance from the top of the cliff to the point where the objects meet is 31.25 meters.
