During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h = - 16 t^{2} + 24 t + 1,$ where h= height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

2.2 and 3.8 secs

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5.4 and 6.2 secs

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.25 and 1.25 secs

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

7 and 5 secs

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 0.25 and 1.25 secs
Given height $= 6 f e e t$
$\Rightarrow - 16 t^{2} + 24 t + 1 = 6$
$\Rightarrow 16 t^{2} - 24 t + 5 = 0$
$\Rightarrow 16 t^{2} - 4 t - 20 t + 5 = 0$
$\Rightarrow 16 t^{2} - 4 t - 20 t + 5 = 0$
$\Rightarrow 4 t (4 t - 1) - 5 (4 t - 1) = 0$
$\Rightarrow (4 t - 1) (4 t - 5) = 0$
$t = \frac{1}{4}, \frac{5}{4}$ or $0.25, 1.25$
So, at time 0.25 secs and 1.25 secs, the ball will be at a height of 6 feet.

Suggest Corrections

Similar questions

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h = - 16 t^{2} + 24 t + 1$ , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h = $- 16 t^{2}$ + 24t + 1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Q. During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation

h = - 16 t^{2} + 24 t + 1

,
where

h = height in feet and t = time in seconds

.
How long does it take for the ball to reach a height of 6 feet?

During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation $h = - 16 t^{2} + 24 t + 1$ , where $h$ = height in feet and $t$ = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Q. During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation

h = - 16 t^{2} + 24 t + 1

, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Join BYJU'S Learning Program

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h=−16t2+24t+1, where h= height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

The correct option is C 0.25 and 1.25 secsGiven height =6feet ⇒−16t2+24t+1=6 ⇒16t2−24t+5=0 ⇒16t2−4t−20t+5=0 ⇒16t2−4t−20t+5=0 ⇒4t(4t−1)−5(4t−1)=0 ⇒(4t−1)(4t−5)=0 t=14,54 or 0.25,1.25 So, at time 0.25 secs and 1.25 secs, the ball will be at a height of 6 feet.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h = - 16 t^{2} + 24 t + 1,$ where h= height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?