Janet jumps off a high diving platform with
a horizontal velocity of 1.84 m/s and lands in
the water 2.9 s later.
How high is the platform? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of m
To find the height of the diving platform, we can use the kinematic equation for vertical motion:
h = v0y * t + (1/2) * a * t^2
where:
h is the height of the platform (what we're trying to find),
v0y is the initial vertical velocity (which is 0 since Janet jumps horizontally),
t is the time of flight (given as 2.9 s), and
a is the acceleration due to gravity (-9.8 m/s^2 since it acts downward).
Since Janet jumps horizontally, her initial vertical velocity is zero, so the equation simplifies to:
h = (1/2) * a * t^2
Substituting the known values:
h = (1/2) * (-9.8 m/s^2) * (2.9 s)^2
h = (1/2) * (-9.8 m/s^2) * 8.41 s^2
h = (-4.9 m/s^2) * 8.41 s^2
h = -41.1599 m^2/s^2
Since the height of the platform cannot be negative, we assume a positive value:
h = 41.16 m
Therefore, the height of the platform is approximately 41.16 meters.