Questions: If a projectile is launched vertically upward from the ground with an initial velocity of 50 ft per sec, then neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s=-16 t^2+50 t. Which equation should be used to determine the time at which the height of the projectile reaches 20 ft ? Choose the correct answer below. A. 20=-16 t^2 B. s=-16(20)^2+50 C. 20=-16 t^2+50 t D. s=-16(20)^2+50(20)

If a projectile is launched vertically upward from the ground with an initial velocity of 50 ft per sec, then neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s=-16 t^2+50 t. Which equation should be used to determine the time at which the height of the projectile reaches 20 ft ?

Choose the correct answer below.
A. 20=-16 t^2
B. s=-16(20)^2+50
C. 20=-16 t^2+50 t
D. s=-16(20)^2+50(20)

Transcript text: If a projectile is launched vertically upward from the ground with an initial velocity of 50 ft per sec, then neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by $s=-16 t^{2}+50 \mathrm{t}$. Which equation should be used to determine the time at which the height of the projectile reaches 20 ft ? Choose the correct answer below. A. $20=-16 t^{2}$ B. $s=-16(20)^{2}+50$ C. $20=-16 \mathrm{t}^{2}+50 \mathrm{t}$ D. $s=-16(20)^{2}+50(20)$

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine the time $ t $ at which the height of the projectile reaches 20 feet. The height $ s $ as a function of time $ t $ is given by the equation:

\[ s = -16t^2 + 50t \]

Step 2: Set Up the Equation

To find the time when the height is 20 feet, we set $ s = 20 $ in the given equation:

\[ 20 = -16t^2 + 50t \]

Step 3: Identify the Correct Equation

We compare the equation we set up in Step 2 with the given options: