Question

A ball rolls down a slope and travels a distance d= t - 0.75t feet in t seconds. Find
the time when the distance travelled by the ball is 11.25 feet.
please answer if you're an ace or a genius.... ​

Answer 1

• The time is $\sf{t\:=\:3.75\:seconds}$

Step-by-step explanation:

Given,

• $\sf{Distance\:(d)\:= t²\:-\:0.75\:t}$
• $\sf{d\:=\:11.25\:= t²\:=\:-0.75}$

$\sf⟼{t²\:-\:0.75\:t\:-\:11.25\:=\:0}$

Here,

• $\sf{a\:=\:1}$
• $\sf{b\:=\:-0.75}$
• $\sf{c\:=\:-11.25}$

Solving,

$\sf⟼\dfrac{-b\pm\sqrt{b^2\:-4\:a\:c}}{2a}$

$\sf⟼\dfrac{(0.75)\pm\sqrt{(-0.75)^2\:-4\:×\:1\:×\:-11.25}}{2\:× \:1}$

$\sf⟼\dfrac{(0.75)\pm\sqrt{0.5625\:+\:45}}{2}$

$\sf⟼\dfrac{0.75\pm\sqrt{45.5625}}{2}$

$\sf⟼\dfrac{0.75\pm{6.75}}{2}$

$\sf⟼\dfrac{7.50}{2}\:or\:{\dfrac{-6}{2}}$

$\sf⟼{3.75}\:or\:{-3}$

$\sf{-3}$ is not possible

$\sf∴{t\:=\:3.75\:sec}$

Hence,

• The time is $\sf{t\:=\:3.75\:seconds}$