A rocket ascends at an angle of 60.0˚ with the horizontal. After 1.00 min it is directly over a point that is a horizontal distance of 12.0 km from the launch point. Find the speed of the rocket.
since cos 60.0˚ = 1/2, it has gone 24 km.
24km/1min = 24 km/min
360
To find the speed of the rocket, we first need to determine the vertical and horizontal components of its velocity.
Given that the angle of ascent is 60.0˚ with the horizontal, we can find the vertical component of velocity by using trigonometry. The vertical velocity component can be calculated using the sine function:
vertical component = velocity * sin(angle)
Since the angle is measured in degrees, we need to convert it to radians before applying the sine function.
The horizontal component of velocity can be found using the cosine function:
horizontal component = velocity * cos(angle)
Now, let's calculate the vertical and horizontal components of velocity.
vertical component = velocity * sin(60.0˚)
horizontal component = velocity * cos(60.0˚)
Using these components, we can determine the distance covered by the rocket in 1.00 min.
The distance covered vertically can be calculated by multiplying the vertical component of velocity by the time taken (1.00 min converted to seconds).
distance vertically = vertical component * time
Given that the horizontal distance from the launch point is 12.0 km, we can use the horizontal component of velocity to calculate the time taken:
time = distance horizontally / horizontal component
Now, let's substitute the given values into the respective equations and solve for the vertical component, horizontal component, and time.
vertical component = velocity * sin(60.0˚)
horizontal component = velocity * cos(60.0˚)
distance vertically = vertical component * (1.00 min converted to seconds)
time = 12.0 km / horizontal component
By rearranging the equations, we can solve for the velocity.
velocity = square root [(vertical component^2) + (horizontal component^2)]
Now, let's plug in the values and calculate the speed of the rocket.