A 60 kg stunt person runs off a cliff at 5.3 m/s and lands safely in the river 11.8 m below. What was the splashdown speed?
To find the splashdown speed of the stunt person, we can use the principle of conservation of energy. The initial kinetic energy of the person when running off the cliff will be converted into potential energy when they reach the maximum height and then further converted into kinetic energy again as they reach the river.
Step 1: Calculate the potential energy at the maximum height.
The potential energy (PE) is given by the formula PE = m * g * h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
PE = 60 kg * 9.8 m/s^2 * 11.8 m
Step 2: Calculate the kinetic energy at the maximum height.
The total energy at the maximum height will be equal to the potential energy, as all the initial kinetic energy has been converted into potential energy.
KE = PE
Step 3: Calculate the kinetic energy at splashdown.
Using the kinetic energy formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity.
KE = 0.5 * 60 kg * v^2
Step 4: Set the kinetic energy at maximum height equal to the kinetic energy at splashdown.
0.5 * 60 kg * v^2 = PE
Step 5: Solve for v (splashdown speed).
v^2 = (2 * PE) / m
v = sqrt((2 * PE) / m)
Step 6: Calculate the splashdown speed.
Substitute the calculated values into the formula:
v = sqrt((2 * (60 kg * 9.8 m/s^2 * 11.8 m)) / 60 kg)
Simplifying the equation:
v = sqrt((2 * 60 * 9.8 * 11.8))
Perform the necessary calculations:
v ≈ 18.84 m/s
Therefore, the splashdown speed of the stunt person is approximately 18.84 m/s.
vetical speed = sqrt (2 g h)
= sqrt (232)
=15.2 m/s
speed = sqrt (15.2^2 + 5.3^2)