Answer to Question #348042 in Physics for mlas

Question

8b.A projectile is launched with an initial speed of 59.0 m/s at an angle of 35.0° above the horizontal. The projectile lands on a hillside 3.55 s later. Neglect air friction. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

(a) What is the projectile's velocity at the highest point of its trajectory?

(b) What is the straight-line distance from where the projectile was launched to where it hits its target?

 

Answer 1

(a)

$$v_x=v_{0x}=v_0\cos\theta\\ =59.0*\cos35.0^\circ=48.3\:\rm m/s$$

$$v_y=0$$

(b)

$$x=v_0\cos\theta t=\\ =59.0*\cos35.0^\circ*3.55=172\:\rm m$$

$$y=v_0\sin\theta t-gt^2/2=\\ =59.0*\sin35.0^\circ*3.55-9.8*3.55^2/2=58.4\:\rm m$$

$$d=\sqrt{x^2+y^2}=\sqrt{172^2+58.4^2}=182\:\rm m$$