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)
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: