LEGO Batman (mass = 0.0051 kg) jumps straight down from a LEGO bridge into a LEG
ID: 1625358 • Letter: L
Question
LEGO Batman (mass = 0.0051 kg) jumps straight down from a LEGO bridge into a LEGO boat (mass = 250 kg) in which a LEGO criminal is fleeing. The velocity of the boat is initially +1.1 m/s. What is the velocity of the boat after Batman lands in it? Two people push a stalled car with a net force of +840 N for 5.0 s. What is a final momentum of the car? If the mass of the car is 1500 kg, what is the final speed of the car? Two arrows are fired horizontally with the same speed of 30 m/s. Each arrow has a mass of 0.100 kg. One is fired due east and the other due south. Find the magnitude and direction of the total momentum of this two-arrow system. Specify the direction with respect to due east Let's say you are camping near an active volcano in a jungle. You are trying to boil water to sterilize it, but you forgot your camp stove and don't have a way to make a fire because everything is wet. Your pot holds 0.20 L of water and the temperature of the water is 25 degrees Celsius. The temperature of the lava of the active volcano is 1200 K (1800 Fahrenheit). How much lava would you have to add to your pot to get the water to reach boiling (373 K, 212 Fahrenheit)?Explanation / Answer
(19) Let the final velocity of the boat be V m/s after the Batman lands on it.
Now apply conservation of momentum -
0.250x1.10 = (0.250+0.0051)xV
=> V = (0.250x1.10) / 0.2551 = 1.08 m/s (Here we have not considered the initial velocity of the Batman because it is in the 90 deg. to the direction of the boat)
(20) Acceration of the car, a = F/m = 840 / 1500 = 0.56 m/s^2
So, the velocity of the car after 5.0 s, v = 0 + 0.56*5 = 2.80 m/s
And the final momentum of the car = m*v = 1500*2.8 = 4200 kg.m/s.
(21) Magnitude of the momentum of each of the arrow, P1 = m*v = 0.10*30 = 3.0 kg.m/s
Now, the total moemtum of the two arrow system in i and j vector system -
P = 3i - 3j
So, magnitude of the total momentum = sqrt[3^2 + 3^2] = 4.24 kg.m/s
And its direction with respect to east = 45 deg.
(22) This is a problem of heat transfer. Q = m*s*delta T
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