Answer:
about 19.6° and 73.2°
Explanation:
The equation for ballistic motion in Cartesian coordinates for some launch angle α can be written ...
y = -4.9(x/s·sec(α))² +x·tan(α)
where s is the launch speed in meters per second.
We want y=2.44 for x=50, so this resolves to a quadratic equation in tan(α):
-13.6111·tan(α)² +50·tan(α) -16.0511 = 0
This has solutions ...
tan(α) = 0.355408 or 3.31806
The corresponding angles are ...
α = 19.5656° or 73.2282°
The elevation angle must lie between 19.6° and 73.2° for the ball to score a goal.
_____
I find it convenient to use a graphing calculator to find solutions for problems of this sort. In the attachment, we have used x as the angle in degrees, and written the function so that x-intercepts are the solutions.
Answer:
The amount of baking powder for each batch
Explanation:
When doing an experiment, we have at least 2 variables involved:
- The independent variable, which is the variable whose value is changed by the operator, to test how the dependent variable will change
- The dependent variable, which is the variable whose value changes depending on the changing in the independent variable, and it is not directly controlled by the operator
For this experiment, we have:
- The amount of baking powder for each batch is the independent variable, since it is changed by Marcie
- The size of the cookies is the dependent variable, since Marcie wants to see how this quantity changes when the independent variable (the amount of baking powder) is changed
It is how forces affect nature
Answer:
(a) θ = 20°
(b) Time Delay = 2.84 s
Explanation:
(a)
This is the case of the projectile motion. In projectile motion, for the same launch speed, the range of a projectile is the same for the complimentary launch angles. Hence, the snowball will have the same range when launched at 70°, at an angle of:
<u>θ = 20°</u>
<u></u>
(b)
The time of flight of snowball can be found by the following formula:
where,
T = Time of flight = ?
u = launch speed = 23.3 m/s
g = acceleration due to gravity = 9.81 m/s²
For θ = 70° :
T₇₀ = 4.46 s
For θ = 20° :
T₂₀ = 1.62 s
Therefore, the time delay can be calculated as follows:
<u>Time Delay = 2.84 s</u>
B is the correct answer because an object moving ten north m/s will turn into 15m/s which as you can tell is accelerating.