MATH SOLVE

5 months ago

Q:
# Math homework that I have no clue how to even approach? Help please.If a stone is thrown down at 130 ft/s from a height of 1,450 feet, its height after t seconds is given by s = 1,450 β 130t β 16t^2.(a) Find its average velocity over the period [1, 4].=___ft/s(b) Estimate its instantaneous velocity at time t = 4. =___ ft/s

Accepted Solution

A:

Answer:a) -210 ft/secb) -258 ft/secStep-by-step explanation:givena) s(t) = - 16tΒ² - 130t + 1450at Β t1 = 1:s(1) = - 16(1)Β² - 130(1) + 1450s(1) = - 16 - 130 + 1450s(1) = 1304at Β t2 = 4:s(2) = - 16(4)Β² - 130(4) + 1450s(2) = - 16(16) - 520 + 1450s(2) = - 256 - 520 + 1450s(2) = 674average velocityVa= [(s(t2) - s(t1)] / (t2 - t1)β Va= (674-1304)/(4-1)= -210 ft/secthe negative sign shows that the ball is moving downwardb) now, instantaneous velocity is give by derivative s'(t) at t s'(t) = - 32t - 130t = 4s'(4) = - 32(4) - 130s'(4) = - 128 - 130s'(4) = - 258therefore instantaneous velocity at t=4 sec= -258 ft/sec