Question

Two marbles are launched at t=0 in the experiment illustrated in the figure below. Marble 1 is launched horizontally with a speed of 4.15 m/s from a height h=0.910m. Marble 2 is launched from ground level with a speed of 5.87 m/s at an angle θ=45.0∘ above the horizontal.

*Where would the marbles collide in the absence of gravity? Give the x coordinate of the collision point?

*Where would the marbles collide in the absence of gravity? Give the y coordinate of the collision point.

*Where do the marbles collide given that gravity produces a downward acceleration of g=9.81m/s2? Give the x coordinate.

*Where do the marbles collide given that gravity produces a downward acceleration of g=9.81m/s2? Give the y coordinate.

Answer 1

The soil is considered as a point of reference. x = 0m and y = 0m.

Positive axis vertically upwards.

Horizontal positive axis to the right (direction of movement)

First the equation of vertical and horizontal position for each marble is established.

For marble 1.

Vertical position equation.

initial velocity

initial position

acceleration

equation

finally

Horizontal position equation

initial position

initial velocity

equation.

finally

for marble 2
decomposition of the initial velocity.

Horizontal

Vertical

Vertical position equation.

initial velocity

initial position

acceleration

equation

Horizontal position equation

initial position

initial velocity

equation.

finally.

When severead acceleration is neglected, only each equation is omitted

*Where would the marbles collide in the absence of gravity? Give the y coordinate of the collision point.

Because there is no gravity, the marble 1 will move horizontally at the same height of y = 0.910m above the ground. As the marble 2 ascends both will be in.

Where would the marbles collide in the absence of gravity? Give the x coordinate of the collision point?

Time it takes the marble 2 to reach the level y = 0.910m

X coordinate

*Where do the marbles collide given that gravity produces a downward acceleration of g=9.81m/s2? Give the x coordinate.

Condition so that it collides. that their vertical positions are equal

combining equations

the time when they meet is

the coordinate y is

Where do the marbles collide given that gravity produces a downward acceleration of g=9.81m/s2? Give the y coordinate.

The horizontal coordinate is equal to

the units are placed in the final operation to understand the units in the results