You are on a diving board and jump up with a velocity of 4.2 m/s. After 1.5 s you land in the water. Assuming a acceleration of -10 m/s and neglecting air resistance:
a) What is your impact velocity?
b) How high is the diving platform?
To find the answers, we can use the kinematic equations of motion.
a) To find the impact velocity, we can use the equation:
vf = vi + at
Where:
vf is the final velocity (impact velocity)
vi is the initial velocity (jump velocity)
a is the acceleration
t is the time
Given:
vi = 4.2 m/s
a = -10 m/s^2 (negative because it is in the opposite direction)
t = 1.5 s
Plugging in the values, we get:
vf = 4.2 m/s + (-10 m/s^2) * 1.5 s
vf = 4.2 m/s - 15 m/s
vf = -10.8 m/s
The impact velocity is -10.8 m/s.
b) To find the height of the diving platform, we can use the equation:
vf^2 = vi^2 + 2gh
Where:
vf is the final velocity (impact velocity)
vi is the initial velocity (jump velocity)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height of the diving platform
Given:
vf = -10.8 m/s
vi = 4.2 m/s
g = 9.8 m/s^2
Plugging in the values, we get:
(-10.8 m/s)^2 = (4.2 m/s)^2 + 2 * 9.8 m/s^2 * h
Simplifying:
116.64 m^2/s^2 = 17.64 m^2/s^2 + 19.6 m/s^2 * h
Rearranging the equation:
19.6 m/s^2 * h = 116.64 m^2/s^2 - 17.64 m^2/s^2
19.6 m/s^2 * h = 99 m^2/s^2
h = 99 m^2/s^2 / 19.6 m/s^2
h = 5.05 m
The height of the diving platform is approximately 5.05 meters.
To calculate the impact velocity and the height of the diving platform, we can use the kinematic equations of motion. The equations are as follows:
v = u + at
s = ut + 0.5at^2
v^2 = u^2 + 2as
Where:
v = final velocity (impact velocity)
u = initial velocity
a = acceleration
t = time
s = distance or height
a) To find the impact velocity:
Given:
Initial velocity (u) = 4.2 m/s
Acceleration (a) = -10 m/s (negative because it opposes the direction of motion)
Time (t) = 1.5 s
Using the equation v = u + at, we can substitute the known values to find the impact velocity (v):
v = 4.2 m/s + (-10 m/s) * (1.5 s)
v = 4.2 m/s - 15 m/s
v = -10.8 m/s
Therefore, the impact velocity is -10.8 m/s. The negative sign indicates that the final velocity is in the opposite direction of the initial velocity.
b) To find the height of the diving platform:
We need to find the distance or height (s) between the diving platform and the water's surface.
Using the equation s = ut + 0.5at^2, we can rearrange the equation to solve for s:
s = ut + 0.5at^2
s = 4.2 m/s * 1.5 s + 0.5 * (-10 m/s) * (1.5 s)^2
s = 6.3 m - 0.75 m
s = 5.55 m
Therefore, the height of the diving platform is approximately 5.55 meters.