Question

5. A rock is tossed from a height of 2 meters at an initial velocity of 30 m/s at an angle of 20° with the ground. Write parametric equations to represent the path of the rock.

Answer 1

x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

Explanation:

The path the rock took can be represented by the following equation x(t) = v0 * cos(θ) * t y (t) = v0 * sin (θ) * t – 0.5 * g * t^2 + h. v0 is the initial velocity (30 m/s), θ is the angle of launch (20 degrees), g is the acceleration due to gravity (9.8 m/s^2) , h is the initial height (2m ) , and t is time. When we switch the values, we get x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

Answer 2

x = 30t cos 20 or x = 28.19t.

y = 30t sin 20 - 4.9t^2 + 2 or y = -4.9t^2 + 10.26t + 2.

Explanation:

The horizontal component of the velocity = 30 cos 20 m/s so the distance at time t seconds = 30t cos 20.

The vertical component is obtained from the equation of motion

s = ut - 1/2* 9.8t^2 + 2

u = 30 sin 20

Vertical component = 30t sin 20 - 4.9t^2 + 2.