<span>So we want to know how much work does Brianna do while climbing the stairs to a height h=8m while she weighs F=425N and in t=6s. So work W is defined as Force F times distance h or: W=F*h. Since Brianna has to use the force that is equal to her own weight during her climbing the calculation is this: W=F*h=425N * 8m=3400J. The work she does is W=3400 J.</span>
The object's kinetic energy changes according to
d<em>K</em>/d<em>t</em> = 15 J/s
If <em>v</em> is the object's initial speed, then its initial kinetic energy is
<em>K</em> (0) = 1/2 (5 kg) <em>v</em> ²
Use the fundamental theorem of calculus to solve for <em>K</em> as a function of time <em>t</em> :

After <em>t</em> = 13 s, the object's kinetic energy is
<em>K</em> (13 s) = 1/2 (5 kg) (13 m/s)² = 422.5 J
Put this as the left side in the equation above for <em>K(t)</em> and solve for <em>v</em> :

==> <em>v</em> ≈ 9.5 m/s
C bases. Have a great day :)
Explanation:
It is given that,
Speed of the ball, v = 10 m/s
Initial position of ball above ground, h = 20 m
(a) Let H is the maximum height reached by the ball. It can be calculated using the conservation of energy as :


h' = 5.1 m
The maximum height above ground,
H = 5.1 + 20
H = 25.1 meters
So, the maximum height reached by the ball is 25.1 meters.
(b) The ball's speed as it passes the window on its way down is same as the initial speed i.e. 10 m/s.
Hence, this is the required solution.