A stone dropped from rest travels 230 feet in the first 5 seconds. How far will it have fallen at the end of 7 seconds? (Round to the nearest Integer)

Question

A stone dropped from rest travels 230 feet in the first 5 seconds. How far will it have fallen at the end of 7 seconds? (Round to the nearest Integer)

Answer 1

The general equation for distance traveled involves initial velocity v_i, time t, and acceleration a:

 

d = v_it + ¹/₂at²

 

 

You've been given d = 230 feet, v_i = 0 feet per second ("from rest"), and t = 5 seconds. Normally, in this type of problem, you'd use gravity as the acceleration. Instead, since acceleration is the only unknown left in the equation, we'll solve for a:

 

230 = (0)(5) + 1/2a(5)²

230 = 0 + 1/2(25)a

460 = 25a

18.4 = a

 

So, acceleration is 18.4 ft/s².

 

Now, using a = 18.4, we'll plug in v_i = 0 and t = 7 and solve for d:

 

d = (0)(7) + 1/2(18.4)(7)²

d = 0 + (9.2)(49)

d = 450.8

 

So, the stone will have fallen 450.8 feet, which rounds up to 451 feet.