How Is Projectile Motion Calculated in Physics?

[kmotoao]

i need help on this problem. thx

A 47.0 kg projectile is launched with an initial speed of 72.0 m/s and an angle of 39.8° above the horizontal. The projectile lands on a hillside 7.15 s later. Neglect air friction. (a) What is the projectile’s kinetic energy at the highest point of its trajectory? (b) What is the height of the impact point? (c) What is its total energy just before it hits the hillside?

 

[Galileo]

For a) Use an energy approach (obiousvly).

$$K=\frac{1}{2}mv_x^2+\frac{1}{2}mv_y^2$$
and $E=K+V$.
You know E from the initial conditions.
At the highest point the velocity in the y-direction is zero.

b) I'd look at the y-component only and write the height as function of time. Then find the height of the impact point.

c) Use conservation of energy again.

 

[wais]

(a) To find the kinetic energy at the highest point of the projectile's trajectory, we can use the equation KE = 1/2mv^2, where m is the mass of the projectile and v is its velocity. Plugging in the given values, we get KE = 1/2(47.0 kg)(72.0 m/s)^2 = 152,064 J. Therefore, the projectile's kinetic energy at the highest point is 152,064 J.

(b) To find the height of the impact point, we can use the equation y = y0 + v0yt - 1/2gt^2, where y0 is the initial height, v0y is the vertical component of the initial velocity, g is the acceleration due to gravity, and t is the time. Since the projectile lands on a hillside, we can assume that the initial height and final height are the same. Also, at the highest point, the vertical component of the velocity is 0. Plugging in the values, we get y = 0 + 0(7.15 s) - 1/2(9.8 m/s^2)(7.15 s)^2 = 247.023 m. Therefore, the height of the impact point is 247.023 m.

(c) The total energy just before the projectile hits the hillside is equal to the sum of its kinetic energy and potential energy. We already calculated the kinetic energy to be 152,064 J. To find the potential energy, we can use the equation PE = mgh, where m is the mass of the projectile, g is the acceleration due to gravity, and h is the height. Plugging in the values, we get PE = (47.0 kg)(9.8 m/s^2)(247.023 m) = 113,709 J. Therefore, the total energy just before the projectile hits the hillside is 152,064 J + 113,709 J = 265,773 J.