The heat gained by the water can be obtained solving the following equation:
where cw = specific heat of water = 4.184 J/gºC
m= mass of water = 1,000 g
ΔT = 2ºC
Replacing these values in (1) we get:
B)
Assuming that the heat energy gained by the water is equal to the one lost by the aluminum, we can use the same equation, taking into account that the energy is lost by the aluminum, so the sign is negative: -8,368 J.
Replacing by the mass of aluminum (125 g), and the change in temperature (-74.95ºC), in (1), we can solve for the specific heat of aluminum, as follows:
⇒
which is pretty close to the Aluminum's accepted specific heat value of 0.900 J/gºC.
Assuming no other forces acting on the ball, from the instant that is thrown vertically downward, it's only accelerated by gravity, in this same direction, with a constant value of -9.8 m/s2 (assuming the ground level as the zero reference level and the upward direction as positive).
In order to find the final speed 2.00 s after being thrown, we can apply the definition of acceleration, rearranging terms, as follows:
We have the value of t, but since the ball was thrown, this means that it had an initial non-zero velocity v₀.
Due to we know the value of the vertical displacement also, we can use the following kinematic equation in order to find the initial velocity v₀:
where Δy = yf - y₀ = 15.4 m - 37.4 m = -22 m (3)
Replacing by the values of Δy, a and t, we can solve for v₀ as follows:
Replacing (4) , and the values of g and t in (1) we can find the value that we are looking for, vf:
Therefore, the speed of the ball (the magnitude of the velocity) as it passes the top of the window is 20.8 m/s.
