5. -/1 points a cannon fires a projectile with an initial velocity of 300 m/s at 59.5° above the horizontal…

5. -/1 points a cannon fires a projectile with an initial velocity of 300 m/s at 59.5° above the horizontal. the projectile impacts a hillside 40.0 s after firing. let the +x - direction be directly ahead of the cannon and the +y - direction be upward. find the x - and y - coordinates of the projectiles impact point, relative to its firing point (in m). x = m y = m assignment scoring your best submission for each question part is used for your score. details my notes ask your teacher

5. -/1 points a cannon fires a projectile with an initial velocity of 300 m/s at 59.5° above the horizontal. the projectile impacts a hillside 40.0 s after firing. let the +x - direction be directly ahead of the cannon and the +y - direction be upward. find the x - and y - coordinates of the projectiles impact point, relative to its firing point (in m). x = m y = m assignment scoring your best submission for each question part is used for your score. details my notes ask your teacher

Answer

Explanation:

Step1: Find initial - horizontal and vertical velocities

The initial velocity $v_0 = 300$ m/s and the launch angle $\theta=59.5^{\circ}$. The initial horizontal velocity $v_{0x}=v_0\cos\theta=300\cos(59.5^{\circ})$ m/s, and the initial vertical velocity $v_{0y}=v_0\sin\theta = 300\sin(59.5^{\circ})$ m/s. $v_{0x}=300\times\cos(59.5^{\circ})\approx300\times0.5075 = 152.25$ m/s $v_{0y}=300\times\sin(59.5^{\circ})\approx300\times0.8616=258.48$ m/s

Step2: Calculate the x - coordinate

The time of flight $t = 40.0$ s. The x - coordinate of the impact point is given by the formula $x=v_{0x}t$. $x = 152.25\times40=6090$ m

Step3: Calculate the y - coordinate

The y - coordinate is given by the kinematic equation $y=v_{0y}t-\frac{1}{2}gt^{2}$, where $g = 9.8$ m/s². $y=258.48\times40-\frac{1}{2}\times9.8\times40^{2}$ $y = 10339.2-7840$ $y = 2499.2$ m

Answer:

$x = 6090$ m, $y = 2499.2$ m