Question

A small object begins a free-fall from a height of H = 89.0 m at to = 0 s. After t = 2.40 s, a second small object is launched vertically up from the ground with an initial velocity of vo = 41.8 m/s. At what height from the ground will the two objects first meet?

a) 72.3 m
b) 54.6 m
c) 38.2 m
d) 62.8 m

Answer 1

The two objects will first meet at a height of 72.1632 m.

Step-by-step explanation:

To find the height at which the two objects first meet, we need to determine the time it takes for the second object to reach that height. We can use the equation for vertical motion:

h = (vo * t) - (0.5 * g * t^2)

Since the second object is launched with an initial velocity of 41.8 m/s and travels for 2.40 s, we can substitute these values into the equation:

h = (41.8 * 2.40) - (0.5 * 9.8 * (2.40^2))

Simplifying the equation gives us:

h = 100.32 - 28.1568

Therefore, the two objects will first meet at a height of 72.1632 m. The correct answer is option a) 72.3 m.