Astudent is running to catch the campus shuttle bus, which is stopped at the bus stop. the student is runnign at a constant speed of 6.0 m/s; she cant run any faster. when trhe student is still 60 m from the bus, it starts to pull away, moving with a constant acceleration of 0.170m/s2. (a) for how much time and what distance does the student have to run at 5.0 m/s before she overtakes the bus? (b) when she reaches the bus, how fast is the bus traveling?

Part a)

Part b)

Explanation:

Part a)

Constant speed by which the student will run is given as

now after some time if student is going to overtake the position of bus

so here the final positions will be same

so we have

so it is

So student will run the total distance

Part b)

Speed of bus when student reach the bus is given as

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft