Answer to Question #104855 in Calculus for Kassim

Question

At a time t seconds after it is thrown up in the air, a tomato is
at a height (in meters) of f(t) = =4.9t
2 +50t +5 m.
A. What is the average velocity of the tomato during the
first 4 seconds? (Include units.)
B. Find (exactly) the instantaneous velocity of the tomato
at t = 4. (Include units.)
C. What is the acceleration at t = 4? (Include units.)
D. How high does the tomato go? (Include units.)
E. How long is the tomato in the air?

Answer 1

A. $\bar{V}= \frac{f(4)-f(0)}{4}=30.4 \frac{m}{c}$

B. $V(t)=f_t'=-9.8t+50$ hence $V(4)=10.8\frac{m}{s}$

C. $a(t)=V_t'=-9.8\frac{m}{s^2}$

D. If$\tau$ is time up then $V(\tau)=0$ hence $-9.8\tau+50=0$ then $\tau=5.1s$ then $f(\tau)=H\approx132.6m$

E. If $t$ is time down then $H=\frac{gt^2}{2}$ hence $t=\sqrt \frac{2H}{g}\approx5.1s$ then $T=t+\tau\approx10.2s$