problem 5: two people are playing the game of horseshoes by throwing horseshoes at the stakes. one person…

problem 5: two people are playing the game of horseshoes by throwing horseshoes at the stakes. one person throws the horseshoe with an initial speed of 12.3 m/s, thrown at an angle of 40° with the horizontal. what is the speed of the horseshoe after 1.3 seconds?

problem 5: two people are playing the game of horseshoes by throwing horseshoes at the stakes. one person throws the horseshoe with an initial speed of 12.3 m/s, thrown at an angle of 40° with the horizontal. what is the speed of the horseshoe after 1.3 seconds?

Answer

Explanation:

Step1: Find the initial horizontal and vertical components of velocity

The initial horizontal - component of velocity $v_{0x}=v_0\cos\theta$ and the initial vertical - component of velocity $v_{0y}=v_0\sin\theta$, where $v_0 = 12.3$ m/s and $\theta = 40^{\circ}$. $v_{0x}=12.3\cos40^{\circ}\approx12.3\times0.766 = 9.42$ m/s $v_{0y}=12.3\sin40^{\circ}\approx12.3\times0.643 = 7.91$ m/s

Step2: Find the vertical component of velocity at $t = 1.3$ s

The equation for the vertical - component of velocity as a function of time is $v_y=v_{0y}-gt$, where $g = 9.8$ m/s². $v_y=7.91-9.8\times1.3=7.91 - 12.74=-4.83$ m/s

Step3: The horizontal component of velocity remains constant

Since there is no acceleration in the horizontal direction (neglecting air - resistance), $v_x = v_{0x}=9.42$ m/s.

Step4: Calculate the speed at $t = 1.3$ s

The speed $v$ is given by $v=\sqrt{v_x^{2}+v_y^{2}}$. $v=\sqrt{(9.42)^{2}+(-4.83)^{2}}=\sqrt{88.74 + 23.33}=\sqrt{112.07}\approx10.6$ m/s

Answer:

$10.6$ m/s