At time 9 s, a car with mass 1400 kg is lo-
cated at <94m, 0 m, 30m> and has momentum
<4500 kg · m/sec, 0 kg · m/sec,−3000 kg · m/sec> .
The car’s momentum is not changing. At time
18 s, find the position of the car:
~d = <dx, dy, dz>
There were 18 kids at the play.Each kid had 4 dolls with them. How many dolls were there?
To find the position of the car at time 18 s, we can use the equation:
~d = ~d0 + (~p/m) * t
where ~d is the position vector, ~d0 is the initial position vector, ~p is the momentum vector, m is the mass of the car, and t is the time.
Given:
Initial position vector, ~d0 = <94m, 0m, 30m>
Momentum vector, ~p = <4500 kg · m/sec, 0 kg · m/sec, -3000 kg · m/sec>
Mass of the car, m = 1400 kg
Time, t = 18s
Using these values in the formula, we can calculate the position vector:
Step 1: Calculate (~p/m) * t
(~p/m) * t = (<4500 kg · m/sec, 0 kg · m/sec, -3000 kg · m/sec> / 1400 kg) * 18s
= <(4500/1400)*18 m, 0 m, (-3000/1400)*18 m>
= <58.286 m, 0 m, -38.571 m>
Step 2: Calculate the final position vector, ~d:
~d = ~d0 + (~p/m) * t
= <94m, 0m, 30m> + <58.286 m, 0 m, -38.571 m>
= <152.286 m, 0 m, -8.571 m>
Therefore, the position of the car at time 18 s is approximately ~d = <152.286 m, 0 m, -8.571 m>.