Please help me, I am in dire need of it,

A football quarterback shows off his skill by throwing a pass {5.70 m downfield and into a bucket. The quarterback consis- tently launches the ball at 38.00' above horizontal, and the bucket is placed at the same level from which the ball is thrown. What initial speed is needed so that the ball lands in the bucket? By how much would the launch speed have to be increased if the bucket is moved to 46.50 m downfield? So I did 5.7cos(38)= 4.49, 2sin(38)/9.8= 0.12 1.23 and 46.50 cos(38)=36.64 did I do this correctly and what shall I do next?

horizontal motion:

46.50=Vi*cos38*time
verticalmotion
hf=hi+vi*sin38*t-1/2 9.8 t^2 hf=hi=0
so have two equations, two unknowns (time t, and vi)
solve for time t in the first eequation, put that into the second equation and solve for vi
a bit of algebra is required.

See previous post: Mon, 10-9-17, 3:36PM.

To solve this problem, you need to analyze the horizontal and vertical components of motion separately.

First, let's analyze the horizontal motion. The ball is thrown 5.70 meters downfield. Since the bucket is at the same level as the launch point, the horizontal distance traveled by the ball is the same as the distance to the bucket. So, the horizontal component of motion can be determined using the formula:

Horizontal distance = Initial horizontal velocity × Time of flight

Since the initial horizontal velocity is the same in both cases, we can say:

(5.70 m) = (Initial horizontal velocity) × (Time of flight for the first case)

To find the initial horizontal velocity, we need to find the time of flight for the first scenario.

Next, let's analyze the vertical motion. The ball is launched at an angle of 38.00 degrees above horizontal. The vertical distance traveled by the ball will be the same as the depth of the bucket in both cases.

So, we can say:

Vertical distance = Initial vertical velocity × Time of flight - 0.5 × Acceleration due to gravity × (Time of flight)^2

Since the initial vertical velocity and acceleration due to gravity are the same in both cases, we can say:

(0 m) = (Initial vertical velocity) × (Time of flight for the first case) - 0.5 × (9.8 m/s^2) × (Time of flight for the first case)^2

Again, to find the initial vertical velocity, we need to find the time of flight for the first scenario.

Solving these two equations will give you the initial horizontal and vertical velocities for the first case. Once you have those, you can calculate the initial speed by using the Pythagorean theorem:

Initial speed = √(Initial horizontal velocity)^2 + (Initial vertical velocity)^2

To find the launch speed needed for the bucket at 46.50 m, you need to repeat the above steps, but with the new distance. Calculate the new initial speed using the same calculations, but substitute 46.50 m for the horizontal distance.

Remember to convert the angles to radians when using trigonometric functions.

I hope this explanation helps you comprehend the steps involved in solving the problem.