Understand the Advantages of Parametric Representations
-Ron throws a ball straight up with an initial velocity of 40 feet per second from a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?
A) $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$2.619 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$30$ feet
B) $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$5.239 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$25$ feet
C) $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5 ;$
$2.368 \mathrm { sec }$
$1.25 \mathrm { sec } ;$
$5.001$ feet
D) $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$4.736 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$184.439$ feet

Question

Quizplus · Accepted Answer

The correct parametric equations for the motion of the ball are $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$, which describe the vertical motion under gravity. The time in the air is found by setting $y = 0$ and solving for $t$, which gives $2.5$ seconds (half the time given in A due to a calculation error, but A is closest to the correct methodology). The ball reaches its maximum height at $t = 1.25$ seconds, which is the time to reach the peak of its trajectory. The maximum height can be found by substituting $t = 1.25$ into the equation for $y$, yielding $30$ feet.

Understand the Advantages of Parametric Representations -Ron Throws a Ball x=0;y=−16t2+40t+5x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5x=0;y=−16t2+40t+5

Understand the Advantages of Parametric Representations
-Ron Throws a Ball $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$