Janet jumps off a high diving platform with a horizontal velocity of 2.71 m/s and lands in water 1.6s later. How high is the platform? Acceleration of gravity is 9.8m/s^2. Answer in units of m.
To find the height of the platform, we can use the equations of motion.
The horizontal velocity of Janet does not affect the height of the platform, so we only need to consider the vertical motion.
We can use the equation:
h = u*t + (1/2)*a*t^2
where:
h is the height of the platform (what we are trying to find)
u is the initial vertical velocity (0 m/s as she is starting from rest)
a is the acceleration due to gravity (-9.8 m/s^2, taking downward direction as negative)
t is the time taken to reach the water (1.6 s)
Substituting the values into the equation:
h = (0)*(1.6) + (1/2)*(-9.8)*(1.6)^2
h = 0 + (1/2)*(-9.8)*(2.56)
h = -4.9*2.56
h = -12.544
Since height cannot be negative, we take the magnitude of the value:
h = |-12.544| = 12.544
Therefore, the height of the platform is approximately 12.544 meters.
To find the height of the diving platform, we can use the principles of projectile motion. Let's break down the problem and find the solution step by step:
Step 1: Identify known values:
- Initial horizontal velocity (Vx) = 2.71 m/s
- Time of flight (t) = 1.6 s
- Acceleration due to gravity (g) = 9.8 m/s^2
Step 2: Calculate the horizontal distance:
Since there is no acceleration or force acting in the horizontal direction, the horizontal distance traveled is given by the formula:
Distance = Velocity * Time
In this case, the horizontal distance traveled is simply:
Distance = Vx * t
Distance = 2.71 m/s * 1.6 s
Distance = 4.336 m
Step 3: Calculate the vertical distance:
To determine the height of the diving platform, we need to find the vertical distance traveled. In projectile motion, the vertical motion can be analyzed independently of the horizontal motion.
Using the equation of motion:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Since Janet jumps horizontally, the initial vertical velocity is 0.
Distance = 0.5 * Acceleration * Time^2
Distance = 0.5 * 9.8 m/s^2 * (1.6 s)^2
Distance = 12.544 m
Step 4: Calculate the height of the platform:
The height of the platform is equal to the vertical distance traveled. So, the height of the platform is 12.544 meters.
Therefore, the height of the diving platform is approximately 12.544 meters.