To find the height of the building, we can use the equation for the vertical displacement of an object in free fall:
d = v₀t + (1/2)gt²
where d is the displacement or height, v₀ is the initial velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, the initial velocity is -25 m/s (since the ball is thrown downwards) and the time is 2.0 s. Plugging in these values, we have:
d = (-25 m/s)(2.0 s) + (1/2)(9.8 m/s²)(2.0 s)²
= -50 m + 19.6 m
= -30.4 m
Since displacement is a vector quantity, the negative sign indicates that the displacement is downwards. Thus, the building is 30.4 meters tall.
13. A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It
strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance?
1 answer