Question

A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37º above the horizontal. Determine the the magnitude and the direction of the velocity at the maximum height.

Answer 1

The magnitude of the velocity at the maximum height is 52.0 m/s and the direction is horizontal.

Step-by-step explanation:

To determine the magnitude and direction of the velocity at the maximum height of a projectile, we need to analyze its motion. At the maximum height, the vertical component of the velocity becomes zero, while the horizontal component remains constant. Since the initial velocity is given as 65.0 m/s at an angle of 37º above the horizontal, we can use trigonometry to determine the horizontal and vertical components of the velocity.

The horizontal component of the initial velocity can be calculated as: Vx = initial velocity * cos(angle) = 65.0 m/s * cos(37º) = 52.0 m/s

At the maximum height, the vertical component of the velocity is zero. We can calculate the vertical component of the initial velocity as: Vy = initial velocity * sin(angle) = 65.0 m/s * sin(37º) = 39.0 m/s

Therefore, at the maximum height, the magnitude of the velocity is 52.0 m/s and the direction is horizontal or along the x-axis.

Answer 2

51.9 m/s, horizontal

Step-by-step explanation:

The horizontal and vertical components of the initial velocity of the projectile are given by:

`v_x = v cos \theta=(65.0 m/s)(cos 37^(\circ))=51.9 m/s\\v_y = v sin \theta=(65.0 m/s)(sin 37^(\circ))=39.1 m/s`

In a projectile motion, the horizontal component of the velocity does not change (because there are no forces acting in the horizontal direction), while the vertical velocity changes according to:

`v_y(t)=v_(0y)-gt`

where g=9.8 m/s^2 is the acceleration due to gravity. However, at the point of maximum height, the vertical velocity is zero (because it is the point at which the projectile starts falling down), so the magnitude of the resultant velocity will simply be equal to the horizontal component:

v = 51.9 m/s

and the direction will be horizontal.