A ball is thrown from a height of
1 answer:
Define
g = 9.8 32.2 ft/s², the acceleration due to gravity.
Refer to the diagram shown below.
The initial height at 123 feet above ground is the reference position. Therefore the ground is at a height of - 123 ft, measured upward.
Because the initial upward velocity is - 11 ft/s, the height at time t seconds is
h(t) = -11t - (1/2)gt²
or
h(t) = -11t - 16.1t²
When the ball hits the ground, h = -123.
Therefore
-11t - 16.1t² = -123
11t + 16.1t² = 123
16.1t² + 11t - 123 = 0
t² + 0.6832t - 7.64 = 0
Solve with the quadratic formula.
t = (1/2) [-0.6832 +/- √(0.4668 + 30.56) ] = 2.4435 or -3.1267 s
Reject the negative answer.
The ball strikes the ground after 2.44 seconds.
Answer: 2.44 s
g = 9.8 32.2 ft/s², the acceleration due to gravity.
Refer to the diagram shown below.
The initial height at 123 feet above ground is the reference position. Therefore the ground is at a height of - 123 ft, measured upward.
Because the initial upward velocity is - 11 ft/s, the height at time t seconds is
h(t) = -11t - (1/2)gt²
or
h(t) = -11t - 16.1t²
When the ball hits the ground, h = -123.
Therefore
-11t - 16.1t² = -123
11t + 16.1t² = 123
16.1t² + 11t - 123 = 0
t² + 0.6832t - 7.64 = 0
Solve with the quadratic formula.
t = (1/2) [-0.6832 +/- √(0.4668 + 30.56) ] = 2.4435 or -3.1267 s
Reject the negative answer.
The ball strikes the ground after 2.44 seconds.
Answer: 2.44 s
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John's method to determine the width of the stream uses the knowledge
that the tangent of 60° is approximately 1.7.
The proper sequence John would use to find the width of the stream are;
- Step 1; <u>John</u><u> drives a stake opposite the tree to establish a line between two points</u>
- Step 2; <u>John uses a </u><u>compass </u><u>to walk away from the stakes at a right angle</u>
- Step 3; <u>On the path John walks until he finds a </u><u>line </u><u>of sight to the tree that equals 60 degrees</u>
- Step 4; <u>John drives a second </u><u>stake </u><u>in the ground</u>
- Step 5; <u>John measures the the </u><u>distance </u><u>between the two stakes</u>
- Step 6; <u>John </u><u>multiplies </u><u>the distance between the two stakes by</u><u> 1.7</u><u> to find the distance</u>.
Reasons:
The steps that can be used to measure the width of the stream are;
Step 1: Drive a stake opposite the tree on the other side of the stream.
Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.
Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.
Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.
Step 5; Measure the distance between the stakes that are placed in the ground.
Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.
<em>The possible question options are;</em>
<em>John measures the the distance between the two stakes</em>
<em>John uses a compass to walk away from the stakes at a right angle</em>
<em>John multiplies the distance between the two stakes by 1.7 to find the distance</em>
<em>John drives a second stake in the ground</em>
<em>On the path John walks until he finds a line of sight to the tree that equals 60 degrees </em>
<em>John drives a stake opposite the tree to establish a line between two points.</em>
Learn more about trigonometric ratios here:
