A toy rocket has a mass of 350 g at launch. The force it produces is 15N and it is fired at an angle of 65 to the horizontal.
What is the initial acceleration of the rocket as a vector.?
To find the initial acceleration of the rocket as a vector, we need to break down the force and mass into their x and y components.
First, we need to find the x and y components of the force. We can use trigonometry to do this:
Fx = F cos(65) = 15 cos(65) = 6.28 N
Fy = F sin(65) = 15 sin(65) = 13.52 N
Next, we need to find the acceleration in each direction. We can use Newton's second law:
F = ma
a = F/m
ax = Fx/m = 6.28 N / 0.35 kg = 17.94 m/s^2
ay = Fy/m = 13.52 N / 0.35 kg = 38.63 m/s^2
So the initial acceleration of the rocket as a vector is:
a = sqrt(ax^2 + ay^2) = sqrt((17.94 m/s^2)^2 + (38.63 m/s^2)^2)
a = 42.31 m/s^2
This means that the rocket is accelerating upward and forward at an angle of 65 degrees to the horizontal, with a magnitude of 42.31 m/s^2.