Question

Player A is running at a velocity of 4 m/s. Player B starts from rest and accelerates at .75 m/s2. If they start from a position 25m apart, how long is it before they collide

Answer 1

Player A is running at a velocity of $4\mathrm{m/s}$. Player B starts from rest and accelerates at $.75\mathrm{m/s2}$. If they start from a position 25m apart, how long is it before they collide?

Coordinate of player A:

$$x _ {A} = 2 5 - 4 t$$

where $t$ - time

Coordinate of player B (he moves with uniform acceleration):

$$x _ {B} = 0. 7 5 t ^ {2}$$

They will collide if:

$$x _ {A} = x _ {B}$$

Or:

$$0. 7 5 t ^ {2} + 4 t - 2 5 = 0$$

Roots of this quadratic equation:

$$t = \frac {- 4 \pm \sqrt {4 ^ {2} - 4 * 0 . 7 5 * (- 2 5)}}{2 * 0 . 7 5} = \frac {2}{3} (- 4 \pm \sqrt {9 1})$$

We need only $t > 0$ roots, so:

$$t = \frac {2}{3} (- 4 + \sqrt {9 1}) \cong 3. 7 s$$

Answer: 3.7 s