Question

1. -/4 points details my notes ask your teacher if you drop an object from a height of 1.7 m, it will hit the ground in 0.59 s. if you throw a baseball horizontally with an initial speed of 45 m/s from the same height, how long will it take the ball to hit the ground? 11. -/4 points details my notes ask your teacher neglecting air resistance, which of the following is true for a ball thrown at an angle to the horizontal? it has a constant velocity in the x direction. it has a constant acceleration in the - y direction. it has a changing velocity in the + y direction. all of the preceding are true.

Explanation:

Step1: Analyze vertical motion

When an object is thrown horizontally, the vertical motion is a free - fall motion. The initial vertical velocity \(v_{0y}=0\ m/s\). The vertical displacement \(y = h\) (height), and the vertical acceleration \(a = g= 9.8\ m/s^{2}\). The equation for vertical displacement is \(y=v_{0y}t+\frac{1}{2}at^{2}\). Since \(v_{0y} = 0\ m/s\), the equation simplifies to \(y=\frac{1}{2}gt^{2}\). The time of flight of a projectile (in the vertical direction) depends only on the vertical displacement and the acceleration due to gravity.

Step2: Determine the time

When an object is dropped from a height \(h = 1.7\ m\) and it takes \(t = 0.59\ s\) to hit the ground. When a baseball is thrown horizontally from the same height \(h = 1.7\ m\), the vertical motion (governed by \(h=\frac{1}{2}gt^{2}\)) is the same as the dropped object. Because the initial vertical velocity \(v_{0y}=0\ m/s\) for both cases (dropped object and horizontally - thrown baseball) and the vertical displacement \(h\) and acceleration \(g\) are the same.

• In the \(x\) (horizontal) direction, neglecting air resistance, there is no acceleration (\(a_x = 0\)). Using the equation \(v_x=v_{0x}+a_xt\), with \(a_x = 0\), we get \(v_x = v_{0x}\) (constant velocity in the \(x\) - direction).
• In the \(y\) (vertical) direction, the acceleration \(a_y=-g=- 9.8\ m/s^{2}\) (constant acceleration in the \(-y\) direction).
• Using the equation \(v_y=v_{0y}+a_yt\), with \(a_y=-g

eq0\), the vertical velocity \(v_y\) (in the \(+y\) or \(-y\) direction depending on the phase of motion) is changing.

Answer:

\(0.59\ s\)

For the second question: