Question
#110
A construction worker drops a full paint can from a height of 500 feet. How fast will the paint can be falling after 2 seconds? A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground? Free-Falling object In Exercises 109 and 110, use the position function s(t) = -4.9 t^2 + 200, which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a seconds is given by lim_t rightarrow a s (a) -s(t)/a - t Find the velocity of the object when t = 3. At what velocity will the object impact the ground? Finding Functions Find two functions f and g such that lim_x rightarrow 0 f(x) and lim_x rightarrow 0 g(x) do not exist, but lim_x rightarrow 0 [f(x) + g(x)] does exist. Proof Prove that if lim_x rightarrow c f(x) exists and lim_x rightarrow e [f (x) + g(x)] does not exist, then lim_x rightarrow c g(x) does not exist. Proof Prove Property 1 of Theorem 2.1. Proof Prove Property 3 of Theorem 2.1. (You may use Property 3 of Theorem 2.2.) Proof Prove Property l of Theorem 2.2. Proof Prove that if lim_x rightarrow c f(x) = 0, then lim_x rightarrow c |f(x)| = 0. Proof Prove that if lim_x rightarrow c f(x) = 0 and |g(x)| lessthanorequalto M for a fixed number M and a x notequalto c, then lim f(x)g(x) = 0.
Explanation / Answer
From the given question,
s(t)=-4.9t2+200 ......................(1)
to get time it takes to hit ground, s(t)=0
0=-4.9t2+200
t=6.39 sec
differentiating (1) both sides
v(t)=-9.8t
replacing t=6.39 sec,
v(t)=(-9.8)(6.39)=62.6 m/s
The object will impact ground with velocity 62.6m/s
