A firecracker explodes into four equal pieces (see figure below). Given the magnitude and direction of the velocity for each piece and the coordinate system shown, determine the x and y velocity components for each piece of the firecracker. (Assume the following:
|v1| = 23.40 m/s,
|v2| = 8.20 m/s,
|v3| = 13.80 m/s,
|v4| = 21.00 m/s,
θ1 = 37°,
and
θ4 = 14°.)
v1
v1x=
v1y=
v2
v2x=
v2y=
v3
v3x=
v3y=
v4
v4x=
v4y=
how are the angles measured?
the angle on coordinateI is 60 degree and on coordinateII is 30degree
V1: v1x=18.69m/s;v1y=14.08m/s
V2: v2x=0m/s; v2y=8.20m/s
V3: v3x=-13.80m/s:v3y=0m/s
V4: v4x= -5.08m/s;v4y=-20.38m/s
To determine the x and y velocity components for each piece of the firecracker, we can use trigonometry. Here's how to calculate the components for each piece:
For v1:
Given |v1| = 23.40 m/s and θ1 = 37°, we can calculate the x and y components using the trigonometric functions cosine and sine.
v1x = |v1| × cos(θ1)
v1y = |v1| × sin(θ1)
Just substitute the values:
v1x = 23.40 m/s × cos(37°)
v1y = 23.40 m/s × sin(37°)
Solve these equations to find the x and y components for v1.
For v2, v3, and v4, follow the same steps:
v2x = |v2| × cos(θ2)
v2y = |v2| × sin(θ2)
v3x = |v3| × cos(θ3)
v3y = |v3| × sin(θ3)
v4x = |v4| × cos(θ4)
v4y = |v4| × sin(θ4)
Remember to substitute the given values for each velocity and angle to solve for the x and y components of velocity.