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 seconds before splashing into the water below. how high is the bridge above the water?how fast is the man going as he hits the water?
use v=u+at to find final velocity
v=final velocity
u=initial velocity = 0 m s^-1
a=acceleration due to gravity=9.8 m s^-2
t=time taken = 3 s
use s=ut + 0.5at^2 to find height
where s= distance travelled
To determine the height of the bridge above the water, we can use the equation for free fall motion:
h = (1/2) * g * t^2
where:
h is the height of the bridge
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time of descent (3 seconds)
Plugging in the values, we can calculate the height:
h = (1/2) * 9.8 * (3^2)
h = (1/2) * 9.8 * 9
h = 44.1 meters
So, the height of the bridge above the water is approximately 44.1 meters.
To determine the speed with which the man hits the water, we can use the equation for velocity:
v = g * t
where:
v is the velocity
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time of descent (3 seconds)
Plugging in the values, we can calculate the velocity:
v = 9.8 * 3
v = 29.4 m/s
So, the man is going approximately 29.4 meters per second as he hits the water.
To calculate the height of the bridge above the water, we can use the basic equation of motion for free fall. In this case, we need to determine the distance traveled during those 3 seconds of descent.
The equation we'll use is:
distance = initial velocity × time + (1/2) × acceleration × time^2
In this scenario, we know that the initial vertical velocity is 0 m/s since the man jumps from rest. We also know that the acceleration due to gravity is approximately 9.8 m/s^2. Plugging these values into the equation, we get:
distance = 0 × 3 + (1/2) × 9.8 × 3^2
distance = (1/2) × 9.8 × 9
distance = 44.1 meters
Hence, the height of the bridge above the water is 44.1 meters.
Now, let's calculate the man's speed as he hits the water. We can consider this speed as the final velocity just before hitting the water. Again, using the equation of motion for free fall, we have:
final velocity = initial velocity + acceleration × time
We know that acceleration is 9.8 m/s^2 and time is 3 seconds. The initial velocity is still 0 since the man starts from rest. Plugging in these values, we get:
final velocity = 0 + 9.8 × 3
final velocity = 29.4 m/s
Therefore, the man's speed as he hits the water is 29.4 meters per second.