how far will a rock fall in 15 sec if it is dropped 150 feet above the river at an initial speed of 24 ft per sec
s(t) = 24t + 16t^2
s(15) = 24*15 + 16*225 = 3960 ft
So, since it fell from only 150 ft, it will fall 150 ft. And, it won't take no steenking 15 seconds to hit the water.
Even if it is thrown upward, and the rock's height is
h(t) = 150+24t-16t^2
it will hit the water in about 4 seconds.
To determine how far the rock will fall in 15 seconds, you can use the formula for the distance an object falls under the influence of gravity:
distance = initial velocity × time + (1/2) × acceleration × time^2
In this case, the initial velocity is 24 feet per second, the time is 15 seconds, and the acceleration due to gravity is approximately 32.2 feet per second squared.
Plugging in the values into the formula:
distance = 24 × 15 + (1/2) × 32.2 × (15)^2
Simplifying the calculation:
distance = 360 + (1/2) × 32.2 × 225
distance = 360 + 8.05 × 225
distance = 360 + 1811.25
distance ≈ 2171.25 feet
Therefore, the rock will fall approximately 2171.25 feet in 15 seconds.