1. No category

Neglecting air resistance, if a ball thrown 4.5 m/s horizontally from a

Neglecting air resistance, if a ball thrown 4.5 m/s horizontally from a 94 m cliff, how far has the
ball fallen after 2.7 seconds?
Solution:
Equation of motion of the ball along the X-axis:
𝑆 = 𝑉π‘₯ 𝑑 +
𝑔π‘₯ 𝑑 2
, 𝑔π‘₯ βˆ’ π‘‘β„Žπ‘’ π‘π‘Ÿπ‘œπ‘—π‘’π‘π‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘‘β„Žπ‘’ π‘”π‘Ÿπ‘Žπ‘£π‘–π‘‘π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘œπ‘› π‘‘β„Žπ‘’ 𝑋 π‘Žπ‘₯𝑖𝑠
2
𝑔π‘₯ = 0, 𝑉π‘₯ = 𝑉, 𝑆 = 𝑉𝑑 = 4.5
π‘š
βˆ— 2.7 𝑠 = 12.15 π‘š
𝑠
Equations of motion along the Y-axis:
𝑔𝑦 𝑑 2
β„Ž = 𝑉𝑦 𝑑 +
, 𝑔𝑦 βˆ’ π‘‘β„Žπ‘’ π‘π‘Ÿπ‘œπ‘—π‘’π‘π‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘‘β„Žπ‘’ π‘”π‘Ÿπ‘Žπ‘£π‘–π‘‘π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘œπ‘› π‘‘β„Žπ‘’ π‘Œ π‘Žπ‘₯𝑖𝑠
2
π‘š
𝑔𝑑 2 9.8 𝑠 2 βˆ— 2.7 𝑠 βˆ— 2.7 𝑠
𝑔𝑦 = 𝑔, 𝑉𝑦 = 0, β„Ž =
=
= 35.721 π‘š
2
2
The distance from the point of throwing by the Pythagorean theorem:
𝐿 = βˆšβ„Ž2 + 𝑆 2 = 37.73 π‘š
Distance above the ground: π‘˜ = 𝐻 βˆ’ β„Ž = 94 π‘š βˆ’ 35.721 π‘š = 58.279 π‘š
Answer: distance above the ground: k = 58.279 m;
distance from the point of throwing: L = 37.73 m;
height of ball fall: h = 35.721 m;
length of the path of the ball along the X axis: S = 12.15 m.

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