Suppose you throw a ball straight up from the ground with a velocity of 224 feet per second. as the ball moves up, gravity slows
1 answer:
Answer:
a) 640 ft
b) 6 seconds (the first time)
c) 14 seconds
Step-by-step explanation:
These problems are solved by using the given equation for the height of the thrown ball with the given values, and solving for the unknown value.
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<h3>a. height after a time</h3>To find the height at a specific time, substitute the time value for t in the height formula and do the arithmetic.
For t = 4, we have ...
h = -16t² +224t = (-16(4) +224)(4) = 160(4) = 640
The height after 4 seconds is 640 ft.
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<h3>b. time for a height</h3>The time required to reach a specific height is found by solving the quadratic equation with h equal to the height value. It can be easier if the equation is in vertex form.
h = -16t² +224t = -16(t² -14t) = -16(t² -14t +49) +784 = -16(t -7)² +784
We want the time to a height of 768 ft, so ...
768 = -16(t -7)² +784
-16/-16 = (t -7)² . . . . . . . . subtract 784, divide by -16
±√1 = t -7 . . . . . . . . . take the square root
t = 7 ±1 = 6 or 8 . . . . . . add 7
The ball will be at a height of 768 ft after 6 seconds, and again after 8 seconds.
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<h3>c. time to reach the ground</h3>The equation from part b applies.
0 = -16(t -7)² +784 . . . . . . . . the height is 0 when the ball is on the ground
-784/-16 = (t -7)² = 49 . . . . . subtract 784, divide by -16
√49 = t -7 . . . . . . . . . . . . . take the positive square root
t = 14 . . . . . . . . . . . . . add 7
The ball will return to the ground after 14 seconds.
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Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and
Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem
Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3. Corresponding angles theorem
and
5. AAA similarity postulates
6. BD over BA Definition of similar triangle