A toy rocket has a mass of 350 g at launch. The force it produces is 15 N and it is fired at an angle of 65 to the horizontal.
What is the initial acceleration of the rocket as a vector.?
We can start by using Newton's second law, which states that force equals mass times acceleration:
F = ma
We know the force (F) is 15 N, and we can convert the mass (m) from grams to kilograms:
m = 0.35 kg
Now we can solve for the acceleration (a) as a vector. However, since the rocket is fired at an angle, we need to break the acceleration vector into its horizontal and vertical components.
The horizontal component of acceleration (ax) is given by:
ax = F * cos(theta) / m
where theta is the launch angle (65 degrees in this case).
ax = 15 N * cos(65 degrees) / 0.35 kg
ax = 10.29 m/s^2
The vertical component of acceleration (ay) is given by:
ay = F * sin(theta) / m - g
where g is the acceleration due to gravity (9.8 m/s^2).
ay = 15 N * sin(65 degrees) / 0.35 kg - 9.8 m/s^2
ay = 12.11 m/s^2
Therefore, the initial acceleration vector of the rocket is:
a = (10.29 m/s^2, 12.11 m/s^2)
Note that the direction of the acceleration vector is not the same as the launch angle, since the rocket will also experience a downward force due to gravity.