Question

The quadratic equation y equals short dash 16 t squared plus 56 t plus 2 represents the height of a projectile, y, in feet, at a particular time, t, in seconds. For what interval or intervals of time will the projectile be above 26 feet?

Answer 1

Answer:

The intervals of time will be $\frac12 \ s$ and 3 s.

Step-by-step explanation:

Given quadratic equation is

$y=-16t^2+56t+2$

where y represents the height in feet, at a particular time, in second.

When a object is thrown upward direction,after a certain time it will attain the height 26 feet. Then when the object comes down it will again attain the height 26 feet.

To find the the time intervals, we put y= 26 in above quadratic equation.

$\therefore26=-16t^2+56t+2$

$\Rightarrow -16t^2+56t+2-26=0$

$\Rightarrow -16t^2+56t-24=0$

$\Rightarrow -8(2t^2-7t+3)=0$

$\Rightarrow (2t^2-7t+3)=0$

$\Rightarrow 2t^2-6t-t+3=0$

$\Rightarrow 2t(t-3)-1(t-3)=0$

$\Rightarrow( 2t-1)(t-3)=0$

$\Rightarrow 2t-1=0 \ or,\ t-3=0$

$\Rightarrow t=\frac12, 3$

The intervals of time will be $\frac12 \ s$ and 3 s.