A toy rocket is launched at an initial velocity of 50 m/s at an angle of 75° with the horizontal. Write parametric equations to represent the path of the rocket.
(A)x = 50t cos 75°y = 50t sin 75° – 4.9t2
(B)x = 50t cos 75°y = 50t sin 75° – 16t2
y = Yo + Vi t - (1/2)gt^2
g = 9.8 so (1/2) g = 4.9
so the last term has to be
-4,9 t^2
The correct parametric equations to represent the path of the rocket are:
(A) x = 50t cos(75°)
y = 50t sin(75°) - 4.9t^2
These equations break down the motion of the rocket into its horizontal (x) and vertical (y) components.
In equation (A), x represents the horizontal distance traveled by the rocket as a function of time (t). It is determined by multiplying the initial velocity (50 m/s) by the cosine of the launch angle (75°). This gives us the horizontal component of the velocity at any given time.
Similarly, in equation (A), y represents the vertical height of the rocket as a function of time (t). It is determined by multiplying the initial velocity (50 m/s) by the sine of the launch angle (75°), and subtracting 4.9 (acceleration due to gravity) multiplied by t^2. This gives us the vertical component of the velocity at any given time, taking into account the downward force of gravity.
Therefore, using these parametric equations, you can calculate the x and y coordinates of the rocket at any given time during its flight.