Janet jumps off a high diving platform with a horizontal velocity of 1.65 m/s and lands in the water 1.8 s later. How high is the platform? The acceleration of gravity is 9.8 m/s2. How far from the base of the platform does she land? Answer in units m
Janet jumps off a high diving platform with a
horizontal velocity of 1.65 m/s and lands in the
water 1.8 s later. How high is the platform? The
acceleration of gravity is 9.8 m/s2. How far from
the base of the platform does she land? Answer
in units m
To find the height of the platform, we can use the equations of motion in vertical direction. Let's break down the information given:
Initial vertical velocity (u) = 0 m/s (since she jumps off with no initial vertical velocity)
Final vertical velocity (v) = ? (we want to find this)
Time taken (t) = 1.8 s
Acceleration due to gravity (g) = 9.8 m/s^2
We can use the kinematic equation:
v = u + gt
Substituting the given values:
v = 0 + (9.8 m/s^2) * (1.8 s)
v = 17.64 m/s
The final vertical velocity (v) is 17.64 m/s. However, since Janet is moving downward, the velocity will have a negative sign. Therefore, v = -17.64 m/s.
Now, to find the height of the platform, we can use another kinematic equation:
v^2 = u^2 + 2as
Since her initial vertical velocity (u) is 0, the equation becomes:
(-17.64 m/s)^2 = 2 * (-9.8 m/s^2) * s
Simplifying:
311.1696 m^2/s^2 = -19.6 m/s^2 * s
Dividing both sides by -19.6 m/s^2:
s = 15.89 m
Therefore, the height of the platform is approximately 15.89 meters.
Next, we can calculate the horizontal distance from the base of the platform where she lands. Since there is no horizontal force acting on Janet, her horizontal velocity remains constant throughout her motion.
The horizontal distance traveled (d) can be calculated using the formula:
d = v_horizontal * t
Given that her horizontal velocity (v_horizontal) is 1.65 m/s and time (t) is 1.8 s:
d = 1.65 m/s * 1.8 s
d = 2.97 m
Therefore, she lands at approximately 2.97 meters from the base of the platform.