Question

In a boat race, boat A is leading boat B by 75 m. At � = 0 s, the speed of boat A is 150 km/h whereas the speed of boat B is 180 km/h. If both boats are accelerating at a constant rate, determine the acceleration of each boat, knowing that at � = 5 s B overtakes A and the speed of A is 180 km/h.

Answer 1

Answer:

$a_A=1.667\:m/s^2\\a_B=4.334\:m/s^2$

Explanation:

$v_{0,A}=150 \:km/hour = 41.667 \:m/s\\v_{0,B}=180 \:km/hour = 50 \:m/s$

$v_A = v_{o,A}+a_At\\50=41.667+5a_A\\a_A=8.333/5=1.667\:m/s^2$

$x_A=v_{0,A}t+\frac{1}{2} a_At^2\\x_A=41.667*5+\frac{1}{2}*1.667*25=229.1725\:m$

$x_B=75+x_A=75+229.1725=304.1725\:m$

$x_B=v_{0,B}t+\frac{1}{2} a_Bt^2\\304.1725=50*5+\frac{1}{2} *a_B*25\\12.5a_B=54.1725\\a_B=4.334\:m/s^2$