Question

An arrow is shot upward at a rate of 220 feet per second. Use the projectile formula h=−16t^2+v_0t to determine when the height of the arrow will be 400 feet. Round your answer to the nearest tenth.

Answer 1

Answer:Explanatory help v

Step-by-step explanation:The question gives you V0 as 220, so plug that in first.

h=-16t2+220t.

Then it says to find the time (solve for t), when the height is 400 ft. Plug 400 ft in as h and solve for t.

400=-16t2+220t.

To solve this, set the quadratic equal to 0 by subtracting 400 from both sides (0=-16t2+220t-400) and use the quadratic formula!

Answer 2

The arrow reaches 400 feet in its way up at about 2.2 seconds after being launched.

Explanation:

Since we want to find the time at which the arrow will reach 400 feet, we use this information in the equation for the height;

`400=-16\,t^2+220\,t\\16\,t^2-220\,t+400=0`

and now use the quadratic equation to solve for the unknown time (t). Notice that been a quadratic equation we expect up to two answers, and then we will need to decide which answer to pick.

`t=(220)/(2\,(16)) +/- (√((-220)^2-4 \,(16)(400)))/(2\,(16)) \\ \\t= 2.156\,sec\,\,\,or\,\,\, t=11.594\,sec`

This means that as the arrow goes up, it takes 2.156 seconds to reach 400 feet, and afterwards, after the arrow reaches it maximum height, it falls back due to acceleration of gravity, going through the same 400 feet height before reaching the ground.

We round the answer to the nearest tenth as requested.