Answer to Question #143119 in Mechanics | Relativity for Mikkos Joshua Garcia

Question

a. A ball is thrown horizontally at 8 m/s. (a) How fast is it moving 2 s later? In what direction is it moving?
b. An airplane is in level flight at a velocity of 300 miles per hour and an altitude of 5000 ft when it drops a bomb. (a) How long does the bomb take to reach the ground? (b) What will the bomb's velocity be on impact?

I need an illustration and complete solution. Thank you

Answer 1

a) Find the vertical velocity $v_y=g\times t = 10\times 2 = 20$ m/s.

Then the ball speed will be $v =\sqrt {v _ y ^ 2 + v _ x ^ 2} =\sqrt {20 ^ 2 + 8 ^ 2 }\approx 21.54$ m/s.

The angle of the ball trajectory in 2 seconds is at an angle to the horizon equal to $\arctg {\frac {20} {8} }\approx 68\degree$ .

b) Since the distance travelled (where $1524$ meters $\approx 5000$ feet) is $S =\frac {g\times t ^ 2} {2}$ , therefore t =\sqrt ${\frac {2\times S} {g}} =\sqrt {\frac {2\times 1524} {10} }\approx17.46$ s

Then the vertical velocity is $v_y=10\times 17.46 = 174.6$ m/s

$300$ miles/hours $\approx134.08$ m/s.

$v_{total}=\sqrt{174.6^2+134.08^2}\approx 220.14$ m/s