A ball is thrown upward with an initial velocity of 35 meters per second from a cliff that is 80 meters high. The height of the ball is given by the quadratic equation h = -49t^2 + 35t + 140 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 60 meters from the ground. Round your answer to the nearest tenth of a second.

Please check your Eq for errors. The -49

should be -4.9.

To find the time when the ball will be 60 meters from the ground, we need to solve the equation h = 60, where h is the height of the ball.

Substituting the value of h in the equation, we have:

-49t^2 + 35t + 140 = 60

To solve this quadratic equation, we can rearrange it to the standard form:

-49t^2 + 35t + 80 = 0

Now, we can use the quadratic formula to find the value of t:

The quadratic formula is given by:

t = (-b ± sqrt(b^2 - 4ac))/(2a)

Here, a = -49, b = 35, and c = 80.

Substituting the values into the formula:

t = (-35 ± sqrt(35^2 - 4(-49)(80)))/(2(-49))

Simplifying further:

t = (-35 ± sqrt(1225 + 15680))/(-98)

t = (-35 ± sqrt(16905))/(-98)

Now, calculate the square root:

t = (-35 ± 130.2)/(-98)

We have two possible solutions:

1. t = (-35 + 130.2)/(-98)
t = 0.974 seconds (rounded to three decimal places)

2. t = (-35 - 130.2)/(-98)
t = 1.584 seconds (rounded to three decimal places)

Since we are looking for the time when the ball will be 60 meters from the ground, we only consider the positive time value, which is:

t = 0.974 seconds (rounded to the nearest tenth of a second)

Therefore, the ball will be 60 meters from the ground approximately 0.974 seconds after it was thrown.