A Challenging Physics Problem: How Long Was the Student Airborne?

How much time was the student airborne if they jumped off a cliff into a river 25.9 m below and landed 20.7 m horizontally away from where they jumped?

The student was airborne for approximately 2.3 seconds.

Calculation of the Time Airborne

To find the time the student was airborne, we need to consider both the horizontal and vertical distances covered during the jump.

First, let's calculate the time using the horizontal distance. The formula for horizontal distance is: d = vt, where d is the distance, v is the horizontal velocity, and t is the time. Given that the student landed 20.7 m horizontally away from the jump point, we can use the formula: 20.7 m = v * t.

Next, let's find the time using the vertical distance. The formula for vertical distance is: d = 0.5 * g * t^2, where d is the vertical distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. Given that the student jumped into a river 25.9 m below, we can use the formula: 25.9 m = 0.5 * 9.8 m/s^2 * t^2.

Solving the equation for t, we get: t = sqrt((2 * 25.9 m) / (9.8 m/s^2)). Calculating the time gives us: t = sqrt(5.28 s^2). Therefore, the student was airborne for approximately 2.3 seconds.