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

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

Step-by-step 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+(1)/(2) a_At^2\\x_A=41.667*5+(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+(1)/(2) a_Bt^2\\304.1725=50*5+(1)/(2) *a_B*25\\12.5a_B=54.1725\\a_B=4.334\:m/s^2`