To find when the player intercepts the ball, we need to set the height of the ball equal to 5 feet and solve for t:
-16t^2 + 42t = 5
-16t^2 + 42t - 5 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -16, b = 42, and c = -5. Plugging these values into the formula:
t = (-42 ± √(42^2 - 4(-16)(-5))) / 2(-16)
t = (-42 ± √(1764 - 320)) / -32
t = (-42 ± √1444) / -32
t = (-42 ± 38) / -32
Now we have two possible solutions for t:
t1 = (-42 + 38) / -32 = -4 / -32 = 1/8
t2 = (-42 - 38) / -32 = -80 / -32 = 2 1/2
Since it doesn't make sense for time to be negative in this context, the correct answer is 2 1/2 seconds after the goalie kicks the ball. Therefore, the answer is:
A. 2 1/2 seconds
During a soccer game, a goalie kicks a ball upward from the ground. The equation h(t)=−16t^2+42t
represents the height of the ball above the ground in feet as a function of time in seconds. When the ball begins moving downward toward the ground, a player from the other team intercepts the ball with his chest 5 feet above the ground. How long after the goalie kicks the ball does the player intercept the ball?
A. 2 1/2
B. 1 5/16
C. 5
D. 1/8
E. 2 5/8
1 answer