Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surface
-A fan in the bleachers at Wrigley Field throws an opposing player's home run baseball back onto the playing field. Assume that the fan is 30 feet above the field and that the ball is launched at an angle of $35 ^ { \circ }$. When will the ball hit the ground if its initial speed is $25 \mathrm { ft } / \mathrm { sec }$ ? Round your answer to the nearest tenth.
A) 2.1 sec
B) 1.9 sec
C) 1.0 sec
D) 4.3 sec

Question

Quizplus · Accepted Answer

We can start by breaking the initial velocity of 25 ft/sec into its horizontal and vertical components. The horizontal component will remain constant throughout the flight, while the vertical component will be affected by gravity. 
Using trigonometry, we can find the initial vertical velocity to be 25*sin(35°) = 14.3 ft/sec and the initial horizontal velocity to be 25*cos(35°) = 20.4 ft/sec. 
Next, we can use the kinematic equation for vertical motion: 
y = y0 + v0*t + 0.5*a*t^2
where y is the vertical position of the ball, y0 is the initial vertical position (30 ft), v0 is the initial vertical velocity (-14.3 ft/sec due to the ball being launched upwards), a is acceleration due to gravity (-32.2 ft/sec^2), and t is the time in seconds. We want to find the time at which y = 0, since that indicates when the ball hits the ground. 
Plugging in the values, we get: 
0 = 30 - 14.3t - 16.1t^2
Simplifying and solving for t using the quadratic formula, we get:
t = 1.9 sec or t = -1.1 sec (ignoring the negative solution because time cannot be negative)
Rounding to the nearest tenth, we get the final answer of 1.9 seconds. So the best choice is B.

Solve the Problem 35∘35 ^ { \circ }35∘ When Will the Ball Hit the Ground If Its

Solve the Problem $35 ^ { \circ }$ When Will the Ball Hit the Ground If Its