Answer:
3.3 seconds
Explanation:
To find the time it takes for the ball to hit the ground, we need to solve the equation y = 0, since the ball will be on the ground when its height (y) is zero.
The equation given is:
y = -16t^2 + 20t + 7
Setting y to zero:
0 = -16t^2 + 20t + 7
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -16, b = 20, and c = 7. Substituting these values into the quadratic formula:
t = (-20 ± √(20^2 - 4(-16)(7))) / (2(-16))
t = (-20 ± √(400 + 448)) / (-32)
t = (-20 ± √848) / (-32)
Simplifying further:
t = (-20 ± √(16 * 53)) / (-32)
t = (-20 ± 4√53) / (-32)
Now we have two possible solutions for t:
t1 = (-20 + 4√53) / (-32)
t2 = (-20 - 4√53) / (-32)
Since time cannot be negative in this context, we can disregard the negative solution.
t ≈ (-20 + 4√53) / (-32)
Calculating this value:
t ≈ 3.3 seconds (rounded to one decimal place)
Therefore, it will take approximately 3.3 seconds for the ball to hit the ground.