Would the baseball clear the fence- projectile motion

[dani123]

Homework Statement

A baseball is hit at a point 1.00m above homeplate. The baseball is given an initial velocity of 35.0m/s at an angle of 45.0° with respect to the horizontal. If the baseball is traveling towards the outfield fence which is 4.0m high and 120m away, will the baseball clear (go over) the fence? If so, by how many maters will it clear the fence? If not, where will the baseball strike?

Homework Equations

d_v=1/2*at²
d_h=V_h*Δt
Kinetic equation d=V_i*t+ 1/2*at²
d_h=-V²*sin2θ /g
sinθ=opp/hyp
cosθ=adj/hyp
Δt=-2Vsinθ / g

The Attempt at a Solution

d_h= cos(45)*35=24.7m
Δt=24.7m/35m/s=0.71s

d=(35)(0.71)+1/2(9.8)(0.71)²=27.3m

No, the baseball will not clear the fence.

I am really lost on this problem just because we are given so many measurements to work with and I don't know the appropriate time to use them and which equation is the right one. If someone could please check my work and correct me and also verify my significant figures that would be greatly appreciated!Thanks so much in advance.

 

[anathema]

Hello,

I would like to offer some guidance on how to approach this problem. First, it is important to identify the given information and what is being asked. In this case, we are given the initial velocity, angle, and position of the baseball, as well as the height and distance of the fence. We are asked to determine if the baseball will clear the fence and if so, by how much.

To solve this problem, we can use the kinematic equations, which relate the position, velocity, and acceleration of an object. It is also helpful to sketch a diagram to visualize the situation.

From the given information, we can calculate the horizontal and vertical components of the initial velocity using the trigonometric equations. The horizontal component will remain constant throughout the motion, while the vertical component will change due to the acceleration of gravity.

Using the given equations, we can calculate the time it takes for the baseball to reach the fence, as well as its vertical position at that time. If the vertical position is greater than the height of the fence, then the baseball will clear the fence.

I would also like to point out that your initial attempt at a solution is missing the effect of gravity on the vertical position of the baseball. Additionally, you should use consistent units throughout your calculations.

I hope this helps and feel free to ask for further clarification if needed. Happy problem solving!