A projectile is launched over level ground at a launch angle of 70o with an initial velocity
vo. At some later time while the projectile is on its way to the peak in its trajectory, its
velocity vector makes an angle of 50o with respect to the horizontal. What is the
magnitude of the projectile’s horizontal velocity at that point?
The horizontal velocity is unchanged
v0 cos70
To find the magnitude of the projectile's horizontal velocity at the point where its velocity vector makes an angle of 50 degrees with respect to the horizontal, we need to use the concept of vector components.
Let's break down the initial velocity of the projectile into its horizontal and vertical components. The launch angle of 70 degrees and the initial velocity (vo) are given. We can calculate the horizontal and vertical components as follows:
Horizontal component (Vx) = vo * cos(angle)
Vertical component (Vy) = vo * sin(angle)
Now, let's consider the situation when the projectile is at the point where its velocity vector makes an angle of 50 degrees with respect to the horizontal. We need to find the magnitude of the horizontal velocity at that point.
From the given information, we know that the angle between the velocity vector and the horizontal is 50 degrees. Since the horizontal velocity is perpendicular to the vertical velocity, the angle between the horizontal velocity and the horizontal line is the complement of 50 degrees, which is 90 - 50 = 40 degrees.
To find the magnitude of the horizontal velocity (Vx'), we can use the equation:
Vx' = V * cos(angle')
where V is the magnitude of the velocity vector and angle' is the angle between the velocity vector and the horizontal.
In this case, the magnitude of the velocity vector (V) remains constant, so Vx' = Vx, the horizontal component of the initial velocity.
So, the magnitude of the projectile's horizontal velocity at the point where its velocity vector makes an angle of 50 degrees with respect to the horizontal is Vx = vo * cos(angle), where angle is 40 degrees.
Remember to convert the angles from degrees to radians when using trigonometric functions if necessary.