3. A projectile is fired from ground level at an angle of 30.0° and a speed of 20.0 m/s. The projectile is fired at a wall 25.0 m away. How far up on the wall will the projectile hit?

Start by finding the time interval, delta t, that it takes for the item to hit the wall. You can do so by knowing that t = d/s. We can solve for s, which is speed, by finding the initial velocity in the horizontal direction.

We can find this by using the launch angle given, 30 degrees, and solving for its horizontal component (parallel to x-axis).

This is found by cos30 = v_x/20

Solve for v_x to get: 17.32051 m/s. Now we can use this initial velocity in the horizontal direction in the equations.

Time = distance/speed

Time = 25 m/17.32051 m/s = 1.44338 seconds

Now we have t = 1.44338 seconds

We want to find the height of the item at a certain time, this time is 1.44338 seconds. We don't have the final velocity, so therefore, we can use the kinematic equation for constant acceleration (object in projectile motion has constant acceleration of -9.8 m/s^2 due to gravity):

No Final Velocity

x_f = x_i + v_i * t + 1/2a (t^2)

x_f and x_i are final and initial positions, respectively, and v_i is the initial velocity. The initial position of this item is 0 m, since we are starting from ground level.

We are trying to solve for the final position, x_f, and we know the variables v_i (17.32051 m/s), t (1.44338 s), and a (9.8 m/s).

Substitute these values into the equation to find the final position:

x_f = (0) + (17.32051 m/s)(1.44338 s) + 1/2(9.8 m/s^2)(1.44338 s)^2

x_f = (25.00007772) + (10.20839454)

x_f = 35.20847227

Now we know that at the time it takes for the item to hit the wall, 1.44338 s, the item's height is 35.20847 meters.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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