Calculate horizontal distance

Question

A shot putter throws the shot with an initial speed of 7 m/s at a 30 Degree angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete’s hand at a height of 1.6m above the ground.

Answer 1

ΔFirst, you have to find the time the shot will be in the air. Do this by finding the vertical portion of the velocity, and using kinematic equations, solve for t.

Second, use the t solved for above and multiply it by the horizontal component of the velocity to get the solution.

v = 7 m/s, θ = 30°, a = -9.81 m/s²

1. v_y,0 = vsinθ = 3.5 m/s
2. using Δx = v_y,0t + gt²/2, find for x = -1.6 (i.e. when the shot is hitting the ground, which is 1.6 m below where it started in the shot putter's hand)
3. -1.6 = 3.5t - 9.81t²/2, solve for t. t = 1.03 s
4. v_x = vcosθ = 6.062 m/s
5. Finally, find the horizontal distance travelled by using the formula vt, which will give distance.
6. d = v_xt = 6.062*1.03 = 6.24 m
7. Answer:
8. d = 6.24 m