Question

A trooper is moving due south along the freeway at a speed of 30 m/s. At time t = 0, a red car passes the trooper. The red car moves with constant velocity of 45 m/s southward. At the instant the trooper's car is passed, the trooper begins to speed up at a constant rate of 2.7 m/s². What is the maximum distance ahead of the trooper that is reached by the red car?

Answer 1

Answer 2

it happens when trooper gets speed 45 m/s

time taken to get 45 m/s, t = (45-30)/2.7

= 5.56 s

maximum distance between troper and car = 45*5.56 - (30*5.56 + 0.5*2.7*5.56^2)

= 41.47 m

Answer 3

s= 250 m

Answer 4

Answer 5

Let us assume trooper will catch red car at t s,

so, distance between two cars,

$s=v_{red}t-v_{troop}t-\frac{1}{2}a_{troop}t^{2}$

$s=45t-30t-0.5\times2.7\timest^{2}$

$s=15t-1.35t^{2}$

for maxima of s,

$\frac{ds}{dt}=0$

$15-2.7t=0$

t=5.55

$\frac{d^{2}s}{dt^{2}}|_{t=5.55}=-2.7<0$

so at t=5.55 s is maximum and the maximum distnace is,

$s_{max}=15\times 5.55-1.35\times 5.55^{2}=41.66m$

Answer 6