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?
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.