Question

How long does it take for the ball thrown vertically upward with an initial velocity of 15 meters per second, following the equation h(t)=15t−5t², to land?

A) 3 seconds
B) 4 seconds
C) 5 seconds
D) 6 seconds

Answer 1

The ball takes 3 seconds to land back on the ground after being thrown vertically upward with an initial velocity of 15 m/s, as found by solving the equation h(t)=15t-5t² for when h(t) equals zero.

Step-by-step explanation:

To determine how long it takes for a ball thrown vertically upward with an initial velocity of 15 meters per second to land, we need to find when the height h(t) equals zero in the equation h(t)=15t−5t². We set the equation to zero and solve for t: 0=15t−5t². This equation can be factored to 0=t(15−5t). The two solutions to this equation are t=0, which is the time at which the ball is thrown, and t=3, which is the time at which the ball lands back on the ground. Therefore, the ball takes 3 seconds to land, corresponding to answer choice A) 3 seconds.