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?

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