# calculus

#### mathelp123

##### New member

Oliver hits a baseball at 3 feet above the ground with an initial speed of 135ft/sec at an angle of 20 degrees with the horizontal.

The outfield wall is 380 feet away and is 15 feet high.

At approximately what height will the ball hit the wall?

I need to rounded to the nearest whole

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

I would begin by resolving the acceleration of the ball into its vertical and horizontal components. Once the ball is in flight, what are the forces acting upon it?

#### Jomo

##### Elite Member
The ball is basically a projectile. You are given the initial speed, the angle over the horizontal and the total distance. What formulas do you have for a projectile?
Please show us some work so we know where you need help.

#### HallsofIvy

##### Elite Member
Neglecting air resistance, the only force here is the force of gravity which, at the surface of the earth, gives a vertical acceleration of -32.2 feet per second per second (negative because it is downward). There is no force, so no acceleration, horizontally. Here there is an initial velocity of 135 feet per second at 20 degrees to the horizontal which means a vertical speed of 135 sin(20) and horizontal speed of 135 cos(20) feet per second. At time t after the start, the horizontal speed is still 135 cos(20) while the vertical speed is 135 sin(20)- 32t feet per second. The horizontal position is 135 cos(20)t and the vertical position is 135 sin(20)t- 16t^2+ 3.

The wall is 380 feet away so solve 135 cos(20)t= 380 for t. Put that value of t into 135 sin(20)t- 16t^2+ 3 to determine the height of the ball at that time.