Question

An object is dropped from a height of 1,600 feet. the amount of time, in seconds, the object takes to hit the ground can be found by solving the equation -16t² + 1,600=0. how many seconds will it take to hit the ground?

A. 10
B. 50
C. 100
D. 10 or -10

Answer 1

To determine how long it takes for the object to hit the ground, we solve the quadratic equation -16t² + 1,600=0, which gives a solution of t = 10 seconds. The negative time value is not considered, as time cannot be negative when measuring the duration of a fall. Option number d is correct.

Step-by-step explanation:

To find out how many seconds it will take for an object dropped from a height of 1,600 feet to hit the ground, we need to solve the quadratic equation -16t² + 1,600=0. In this case, the object is under the influence of gravity, which is represented by the acceleration due to gravity (g) in the United States rounding to 32 feet per second per second (ft/s²).

However, in the equation, we have a negative sign because the object is falling downwards, which is -16 ft/s² when halved in the equation. To solve for t, we divide both sides by -16, obtaining t² = 100. Taking the square root of both sides gives us t = 10 seconds. Since time can't be negative in this context, we dismiss the negative root, which would be -10 seconds.