Answer to Question #183728 in Algebra for Hailee R

Question

For times t >0 in seconds, a police car is patrolling a local street. The position along the straight, flat road is given in meters by the function P t( )=25t. Directly ahead of the police car, a bank robber’s getaway car begins to speed up to leave the scene of the crime. The getaway car’s position along the road is given in meters by the function G t( )= + 75 2 5t 2 . . Graph the functions P t( ) and G t( ) on the same set of axes. What conclusion can you draw? Does the police car catch the getaway car? Determine the time at which the police car intersects the getaway car, or determine how close the police car gets to the getaway car before the bank robber evades capture

Answer 1

let,

Position of Police car : $y=25t$

Position of  robber’s getaway car: $y=75-2.5t^2$

the position of where police catch robber is where graph intersect each other and t>0.

and we can find point by equating both the equations.

$\bigstar$ from graph and equations we get point as...

(2.416 , 60.405)

$\bigstar$ we conclude that yes the police car intersect robber's car.

$\bigstar$ implies$\implies$ police will catch robber at

$\boxed{position =60.405 }$

at

$\boxed{ time =2.416 sec.}$