Solve.
-A ball is thrown downward with an initial velocity of 42 meters per second from a cliff that is 100 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 42 t + 120$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground. Round your answer to the nearest tenth of a second.
A) $2.0$ seconds
B) $1.8$ seconds
C) $2.9$ seconds
D) $1.9$ seconds

Question

Quizplus · Accepted Answer

The ball will be 20 meters from the ground when $h = 20$. Substituting this into the equation, we get:$$20 = - 4.9 t ^ { 2 } - 42 t + 120$$$$0 = - 4.9 t ^ { 2 } - 42 t + 100$$Using the quadratic formula, we get:$$t = \frac { - ( - 42 ) \pm \sqrt { ( - 42 ) ^ { 2 } - 4 ( - 4.9 ) ( 100 ) } } { 2 ( - 4.9 ) }$$$$t = \frac { 42 \pm \sqrt { 1764 + 1960 } } { - 9.8 }$$$$t = \frac { 42 \pm \sqrt { 3724 } } { - 9.8 }$$$$t = \frac { 42 \pm 61 } { - 9.8 }$$$$t = \frac { 42 + 61 } { - 9.8 } \quad \text{or} \quad t = \frac { 42 - 61 } { - 9.8 }$$$$t = \frac { 103 } { - 9.8 } \quad \text{or} \quad t = \frac { - 19 } { - 9.8 }$$$$t \approx 10.5 \quad \text{or} \quad t \approx 1.9$$Since the ball cannot be 20 meters from the ground before it is thrown, the only valid solution is $t \approx 1.9$.

Solve -A Ball Is Thrown Downward with an Initial Velocity h=−4.9t2−42t+120h = - 4.9 t ^ { 2 } - 42 t + 120h=−4.9t2−42t+120

Solve
-A Ball Is Thrown Downward with an Initial Velocity $h = - 4.9 t ^ { 2 } - 42 t + 120$