Is it possible for the friend on the balcony to catch the keys thrown by the college student? If not, what distance will the keys reach?
It is unlikely that the friend on the balcony will be able to catch the keys thrown by the college student. To determine whether the keys can be caught or not, we need to calculate the time it takes for the keys to reach the balcony, as well as the height they will reach. Let's break down the problem and find the solution step by step.
Calculating the time it takes for the keys to reach the balcony
To calculate the time it takes for the keys to reach the balcony, we can use the kinematic equation for the vertical motion of an object:
Δy = v₀t + (1/2)at²
Where:
Δy = vertical displacement (6m)
v₀ = initial vertical velocity (9.4 m/sec)
a = acceleration due to gravity (-9.8 m/s²)
t = time
Plugging in the values, we get:
6 = 9.4t + (1/2)(-9.8)t²
6 = 9.4t - 4.9t²
Rearranging the equation, we get a quadratic equation:
4.9t² - 9.4t + 6 = 0
Solving this quadratic equation will give us the time it takes for the keys to reach the balcony.
Finding the distance the keys will reach
To find the distance the keys will reach, we can use the formula:
Distance = Initial velocity × Time
Once we have calculated the time it takes for the keys to reach the balcony, we can plug it back into this formula to find the distance they will reach if they are not caught by the friend on the balcony.
By going through these calculations, we will be able to determine whether the friend can catch the keys or not, and if not, we will find out the distance the keys will reach. It's important to understand the concepts of projectile motion and kinematic equations to solve this problem accurately.