Old Isaac took a little nosedive from his perch on Mrs. Cohen’s window ledge 25 feet above ground. Given that he fell as a result of a gentle tap to his noggin, how fast is Isaac traveling when he hit’s the ground? (gravity is -32ft/sec^2).
25ft=½(32ft/sec^2)t^2
t=1.25sec
-32ft/sec=(vf - 0)/1.25s
Vf=-40ft/sec
or you could have worked it ..
Vf^2=2*g*height
Vf= sqrt (2gh)=sqrt(2*32*25)=sqrt (1600)
To calculate Isaac's speed when he hits the ground, we can use the equation:
Vf = Vi + at
Where:
- Vf is the final velocity (speed) when he hits the ground
- Vi is the initial velocity (which is 0 in this case, as he was at rest before falling)
- a is the acceleration due to gravity (which is -32 ft/sec^2, negative because it acts downwards)
- t is the time it takes for him to fall (which we have calculated to be 1.25 seconds)
Plugging in the values, we have:
Vf = 0 + (-32 ft/sec^2) * 1.25 sec
Vf = -40 ft/sec
Therefore, Isaac is traveling at a speed of -40 ft/sec when he hits the ground. The negative sign indicates that the velocity is directed downward.
To calculate the speed at which Isaac is traveling when he hits the ground, we can use the kinematic equation:
vf = vi + at
Where:
- vf is the final velocity,
- vi is the initial velocity,
- a is the acceleration,
- t is the time.
In this case, the initial velocity is 0 ft/sec since Isaac starts from rest, and the acceleration due to gravity is -32 ft/sec^2 (negative because it acts in the downward direction).
We already found that it takes Isaac 1.25 seconds to fall to the ground (t = 1.25 sec).
Substituting these values into the equation:
vf = 0 + (-32 ft/sec^2)(1.25 sec)
= -40 ft/sec
Therefore, when Isaac hits the ground, he is traveling at a speed of -40 ft/sec (negative indicating that he is moving downwards).