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>
constant velocity components
Vx = 4500/1400
Vy = 0
Vz = -3000/1400
goes for 18-9 or 9 seconds
distance = speed*time
so
x = 94 + 9*4500/1400
y = 0 + 0
z = 30 -9(3000/1400)
To find the position of the car at time 18 seconds, we can use the concept of momentum and its relationship with velocity and position.
Step 1: Finding the velocity of the car
Given that mass (m) of the car is 1400 kg and momentum (p) at time 9 seconds is <4500 kg · m/sec, 0 kg · m/sec,−3000 kg · m/sec>, we know that momentum is defined as the product of mass and velocity: p = m * v.
So, to find the velocity (v), we can rearrange the equation as v = p / m.
For each component of velocity, we have:
vx = px / m = 4500 kg · m/sec / 1400 kg
vy = py / m = 0 kg · m/sec / 1400 kg
vz = pz / m = -3000 kg · m/sec / 1400 kg
Calculate these values to find the velocity of the car.
Step 2: Finding the change in position
Since the car's momentum is not changing, it means that the net force acting on it is zero, and therefore it is moving with a constant velocity from time 9 seconds to time 18 seconds.
We can calculate the change in position (∆d) using the formula: ∆d = v * ∆t, where v is the velocity and ∆t is the time interval.
∆dx = vx * ∆t = vx * (18 s - 9 s)
∆dy = vy * ∆t = vy * (18 s - 9 s)
∆dz = vz * ∆t = vz * (18 s - 9 s)
Calculate these values to find the change in position (∆d).
Step 3: Finding the final position
Now, to find the final position of the car at time 18 seconds, we need to add the change in position (∆d) to the initial position of the car at time 9 seconds.
Final position = Initial position + ∆d
So, the final position of the car is:
~d = <dx, dy, dz> = <94m, 0m, 30m> + <∆dx, ∆dy, ∆dz>
Plug the calculated values of ∆dx, ∆dy, and ∆dz into this equation to find the final position of the car.