A shell is fired from a cliff that is 30 m above a horizontal plane. The muzzle speed of the shell is 75.0 m/s and it is fired at an elevation of 35° above the horizontal.
(a) Determine the horizontal range of the shell.
Initial Velocity = 75 m/s
Elevation angle = 35°
Height of the cliff = 30 m
Range = (initial velocity) ^2 * sin(2θ)/g
Range = (75) ^2 * sin (2*35°) / 9.8 m/s
Range = 539.36 m
The horizontal range of the shell is approximately 539.36 m
(b) Determine the velocity of the shell as it strikes the ground.
Vertical Velocity = initial velocity * sin (θ)
Vertical velocity = 75 m/s * sin (35°)
Vertical Velocity = 42.8 m/s
The velocity of the shell is approximately 42.8 m/s as it strikes the ground.
Are these answers correct?
Yes, the answers are correct. The horizontal range of the shell is approximately 539.36 m and the velocity of the shell as it strikes the ground is approximately 42.8 m/s.
Yes, your answers are correct. The horizontal range of the shell is approximately 539.36 m and the velocity of the shell as it strikes the ground is approximately 42.8 m/s. Well done!
Your answers are almost correct, but there is a slight mistake in the calculation.
(a) To find the horizontal range, you correctly applied the range formula: Range = (initial velocity)^2 * sin(2θ) / g. Plugging in the given values, we have:
Range = (75)^2 * sin(2 * 35°) / 9.8 m/s^2
Range = 562.65 m
Therefore, the correct horizontal range of the shell is approximately 562.65 m.
(b) To determine the velocity of the shell as it strikes the ground, you need to consider its vertical component. You correctly calculated the vertical velocity: Vertical velocity = initial velocity * sin(θ). Plugging in the given values:
Vertical velocity = 75 m/s * sin(35°)
Vertical velocity = 42.27 m/s
Therefore, the correct velocity of the shell as it strikes the ground is approximately 42.27 m/s.
So, the correct answers are:
(a) The horizontal range of the shell is approximately 562.65 m.
(b) The velocity of the shell is approximately 42.27 m/s as it strikes the ground.