a man jumps off a bridge to see how high it is. he measures his time of descent. he is in the air for 3.0 s before splashing into the water below.
a. How high is the bridge above the water?
b. How fast is the man going as he hits the water?
To determine the height of the bridge above the water, we can use the equation of motion for free fall:
h = 0.5 * g * t^2,
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and t is the time of descent.
a. To find the height of the bridge, we substitute the values into the equation:
h = 0.5 * 9.8 m/s^2 * (3.0 s)^2
= 0.5 * 9.8 m/s^2 * 9.0 s^2
= 44.1 m.
Therefore, the height of the bridge above the water is approximately 44.1 meters.
b. To find the speed at which the man hits the water, we can use the equation:
v = g * t,
where v is the final velocity.
b. Substituting the values, we have:
v = 9.8 m/s^2 * 3.0 s
= 29.4 m/s.
Therefore, the man is going approximately 29.4 meters per second as he hits the water.