Janet jumps off a high diving platform with
a horizontal velocity of 2.23 m/s and lands in
the water 1.7 s later.
How high is the platform? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of m
h = 0.5g*t^2 = 4.9*1.7^2 = 14.2 m.
To find the height of the platform, we can use the kinematic equation:
Y = Y0 + V0y*t - (1/2) * g * t^2
Where:
- Y is the height of the platform (what we're trying to find)
- Y0 is the initial height (which we assume to be zero since she jumps off the platform)
- V0y is the vertical component of the initial velocity (since she jumps horizontally, V0y = 0)
- g is the acceleration due to gravity (which is -9.8 m/s^2 because it acts downwards)
- t is the time taken to reach the water (which is 1.7 seconds)
Substituting the known values:
Y = 0 + (0) * (1.7) - (1/2) * (-9.8) * (1.7)^2
Simplifying the equation:
Y = 0 + 0 - 0.5 * (-9.8) * (2.89)
Y = 0.5 * 9.8 * 2.89
Y = 14.21 meters
Therefore, the height of the platform is approximately 14.21 meters.